Gr 10 Math Ch 2 SUM: Exponents, Equations and Inequalities

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What must be done to both sides of a linear inequality when dividing by a negative number?

The inequality sign must be switched. (correct)

The inequality sign remains the same.

Both sides must be multiplied by the negative number.

You can ignore the inequality sign.

What is the first step to take when the unknown variable is in the denominator of the equation?

Divide both sides by the variable in the denominator.

Rearrange the equation to eliminate the denominator.

Multiply both sides by the lowest common denominator. (correct)

Add both sides by the other side of the equation.

Which of the following is a valid linear inequality?

$2x + 1 ext{ is greater than } 3$

$x^2 + 3 eq 5$

$3x - 4 ext{ less than or equal to } 5x + 1$

5x + 2 < 7 (correct)

In the inequality $rac{4}{3}x - 6 < 7x + 2$, what is the initial operation needed to isolate x?

Subtract 7x from both sides. Signup and view all the answers

What can be concluded if an inequality simplifies to a false statement, such as 6 < 2?

The original inequality has no solution. Signup and view all the answers

What is the result of simplifying the expression $a^3 imes a^4$?

$a^{7}$ Signup and view all the answers

What is the simplified form of $rac{a^5}{a^2}$?

$a^{3}$ Signup and view all the answers

According to the laws of exponents, what is $(xy)^3$ equal to?

$x^3y^3$ Signup and view all the answers

What is the value of $a^0$ when $a eq 0$?

1 Signup and view all the answers

What is $a^{-3}$ equal to?

$rac{1}{a^3}$ Signup and view all the answers

How do you simplify the expression $rac{(ab)^2}{(a^2b^2)}$?

$1$ Signup and view all the answers

What does the expression $(rac{a}{b})^2$ become?

$rac{a^2}{b^2}$ Signup and view all the answers

What is the greatest common factor (GCF) of the expression $a^4 + a^3$?

$a^3$ Signup and view all the answers

What is the first step for solving a quadratic equation?

Rewrite the equation in standard form Signup and view all the answers

In the factorisation method for solving quadratic equations, what is the purpose of setting each factor equal to zero?

To solve for the variable Signup and view all the answers

When solving simultaneous equations by substitution, what is the first step?

Express one variable in terms of the other Signup and view all the answers

What is a necessary condition for solving simultaneous equations?

There must be an equal number of equations and variables Signup and view all the answers

Which method involves adding or subtracting two equations to eliminate a variable?

Elimination method Signup and view all the answers

What step is NOT part of solving word problems using algebra?

Investigating similar problems Signup and view all the answers

What does a literal equation represent?

An equation defining relationships between several variables Signup and view all the answers

Which operation should be performed to isolate an unknown variable in a literal equation?

Perform the opposite operation for each term Signup and view all the answers

What is the graphical solution to simultaneous equations?

The intersection of the two graphs Signup and view all the answers

What is the last step in the process of solving quadratic equations?

Check the solution Signup and view all the answers

What is the result of multiplying $a^{2/3}$ by $a^{4/5}$?

a^{22/15} Signup and view all the answers

How would you simplify $rac{a^{3/4}}{a^{5/6}}$?

a^{(3/4 - 5/6)} Signup and view all the answers

Which of the following is the correct application of the power of a power property?

(a^{1/2})^{1/3} = a^{1/6} Signup and view all the answers

What is the value of $x$ in the equation $2^x = 32$?

5 Signup and view all the answers

When solving the exponential equation $3^x = 81$, which method would best apply?

Setting the exponents equal after writing as $3^x = 3^4$ Signup and view all the answers

What is the highest exponent of the variable in a linear equation?

At most 1 Signup and view all the answers

What is a possible scenario in a quadratic equation?

It has just one solution. Signup and view all the answers

Which step is NOT part of solving a linear equation?

Set exponents equal Signup and view all the answers

In what condition can logarithms be used to solve exponential equations?

When bases are not easily made the same Signup and view all the answers

What is the result of simplifying $(xy)^{1/2}$?

x^{1/2} * y^{1/2} Signup and view all the answers

What is the first step when solving a quadratic equation using factorisation?

Rewrite the equation in standard form Signup and view all the answers

Which method involves expressing one variable in terms of the other?

Substitution Signup and view all the answers

What ensures that a quadratic equation is balanced during manipulation?

Perform the same operation on both sides Signup and view all the answers

In solving simultaneous equations graphically, what does the solution represent?

The coordinates of intersection points Signup and view all the answers

What is one way to check the correctness of a solution to a quadratic equation?

Substitute the solution back into the original equation Signup and view all the answers

When solving a literal equation, what should you do to isolate the unknown variable?

Change the subject of the formula Signup and view all the answers

Which statement best describes simultaneous equations?

They require two equations for two unknown variables Signup and view all the answers

What is a key consideration when writing equations to solve word problems?

Translate words into expressions Signup and view all the answers

In the elimination method for solving simultaneous equations, what is the goal?

Eliminate one variable by making coefficients equal Signup and view all the answers

What must you remember when isolating a variable by taking a square root?

Both positive and negative solutions must be considered Signup and view all the answers

Which expression correctly simplifies according to the laws of exponents?

$a^5 \times a^2 = a^7$ Signup and view all the answers

What is the result of applying the negative exponent law to the expression $a^{-3}$?

$\frac{1}{a^3}$ Signup and view all the answers

Which of the following represents the correct application of the division law of exponents?

$\frac{a^{-2}}{a^3} = a^{-5}$ Signup and view all the answers

When simplifying the expression $(ab)^4$, what is the resulting form?

$a^4 b^4$ Signup and view all the answers

How can the expression $\frac{(xy)^3}{x^2 y^3}$ be simplified?

$x^{3-2} y^{3-3}$ Signup and view all the answers

What is the simplified form of the expression [\frac{6a^4b^2}{3a^2b}]?

$2a^2b$ Signup and view all the answers

Which expression represents the difference of squares correctly?

$a^2 - b^2 = (a - b)(a + b)$ Signup and view all the answers

What is the significance of applying the zero exponent law?

$a^0 = 1$ for any $a \neq 0$ Signup and view all the answers

What is the correct expression for raising a product to a power according to the laws of rational exponents?

(ab)^{m/n} = a^{m/n} b^{m/n} Signup and view all the answers

Which method is used to solve exponential equations when the bases cannot be made the same?

Using logarithms Signup and view all the answers

What does the equation $a^{m/n} imes a^{p/q}$ simplify to based on the multiplication of exponents rule?

a^{m/n + p/q} Signup and view all the answers

What must be done first to solve a linear equation?

Expand all brackets Signup and view all the answers

When can it be concluded that $x = y$ in the context of exponential equations?

When $a^x = a^y$ and $a > 0$, $a eq 1$ Signup and view all the answers

How many solutions can a quadratic equation typically have?

At most two solutions Signup and view all the answers

In the power of a power property, how is $(a^{m/n})^{p/q}$ expressed?

a^{mp/nq} Signup and view all the answers

What operation should be performed to isolate the variable when solving a linear equation?

Add or subtract constant terms Signup and view all the answers

To simplify a rational exponent such as $ rac{a^{3/4}}{a^{5/6}}$, what should be done with the exponents?

Subtract the exponents: $3/4 - 5/6$ Signup and view all the answers

What must be done first when solving the inequality $rac{3x + 1}{2} geq 4$?

Multiply both sides by 2 Signup and view all the answers

Which inequality correctly represents the result of dividing both sides of $8 > 6$ by -2?

$-4 < -3$ Signup and view all the answers

In the inequality $2 - x geq 3$, what is the correct first operation to isolate $x$?

Subtract 2 from both sides Signup and view all the answers

When manipulating the inequality $rac{4}{3}x - 6 < 7x + 2$, what initial step is required?

Multiply all terms by 3 Signup and view all the answers

What is the correct interpretation if an equation like $6 < 2$ results from solving a linear inequality?

The inequality has no solutions Signup and view all the answers

What must be done to both sides when solving the inequality $2 - x \geq 3$?

Subtract 2 from both sides Signup and view all the answers

When a linear inequality such as $\frac{3x + 1}{2} \geq 4$ is presented, what is the first step to solve it?

Multiply both sides by 2 Signup and view all the answers

In solving the inequality $\frac{4}{3}x - 6 < 7x + 2$, what should be done first to isolate x?

Subtract 7x from both sides Signup and view all the answers

What is true about the operation performed on both sides of the inequality when dividing by a negative number?

The inequality sign must be switched Signup and view all the answers

For the inequality $8 > 6$, what happens if both sides are divided by -2?

The direction of the inequality changes Signup and view all the answers

What does the expression $a^{-n}$ equal to?

$rac{1}{a^n}$ Signup and view all the answers

When simplifying the expression $a^5 imes a^2$, what is the result?

$a^{7}$ Signup and view all the answers

To simplify $(rac{3}{2})^3$, which law of exponents should be applied?

Power of a Quotient Signup and view all the answers

What is the simplified result of the expression $rac{a^4 imes a^3}{a^5}$?

$a^{1}$ Signup and view all the answers

Which expression correctly applies the law of exponents to simplify $(a^2b^3)^2$?

$a^{4}b^{6}$ Signup and view all the answers

What is the outcome when simplifying the expression $rac{(ab)^4}{a^2b^3}$?

$a^{2}b^{1}$ Signup and view all the answers

What does the zero exponent law state?

$a^0 = 1$ Signup and view all the answers

When applying the law of exponents, what is true about raising a number to a negative exponent?

It is equivalent to taking the reciprocal. Signup and view all the answers

How can the expression $a^{1/2} imes a^{3/4}$ be simplified?

$a^{5/4}$ Signup and view all the answers

What is the result when the expression $(rac{2}{3})^{1/2}$ is simplified?

$rac{2^{1/2}}{3^{1/2}}$ Signup and view all the answers

If $2^x = 2^5$, what can be concluded about the variable $x$?

$x = 5$ Signup and view all the answers

When solving the equation $3^{x} = 27$, which approach is most useful?

Convert $27$ to the same base as $3$ before equating exponents. Signup and view all the answers

Which of the following shows the correct method for simplifying the expression $rac{a^{5/6}}{a^{1/3}}$?

$a^{(5/6) - (1/3)}$ Signup and view all the answers

What is the characteristic of a quadratic equation?

It can have two or more solutions. Signup and view all the answers

Which of the following options illustrates the power of a power property incorrectly?

$ig(a^{p}ig)^{m/n} = a^{p/m+n}$ Signup and view all the answers

If an exponential equation simplifies to $4 < 2$ after manipulation, what does it indicate?

There are no solutions. Signup and view all the answers

Which method should be used to solve the equation $x^2 - 5x + 6 = 0$?

Factoring Signup and view all the answers

When solving linear equations, what should be done first?

Rearranging the terms. Signup and view all the answers

What is the correct order of operations when rewriting a quadratic equation for factorisation?

Rewrite it in standard form, then factorise, and finally solve for x. Signup and view all the answers

What does substituting into the second equation achieve when solving simultaneous equations by substitution?

It reduces the problem to one equation with one variable. Signup and view all the answers

What must be ensured when performing operations on one side of a quadratic equation?

The equation must remain balanced on both sides. Signup and view all the answers

What is the main goal of using the elimination method in solving simultaneous equations?

To make the coefficients of one variable the same. Signup and view all the answers

When solving a literal equation, what is the first action to isolate the unknown variable?

Perform the opposite operation of what is applying to the variable. Signup and view all the answers

Which step is NOT part of the problem-solving strategy for word problems?

Finding all possible solutions regardless of constraints. Signup and view all the answers

What is the graphical solution to simultaneous equations visually represented as?

The point where the graphs of the equations intersect. Signup and view all the answers

Why is checking the solution important after solving a quadratic equation?

To verify that the solution satisfies the original equation. Signup and view all the answers

When rearranging a literal equation, what must be considered about the terms containing the unknown variable?

They should be factored out if in multiple terms. Signup and view all the answers

What role does dividing by common factors play in solving a quadratic equation?

It helps simplify the equation if applicable. Signup and view all the answers

What must occur to the inequality sign when both sides of a linear inequality are multiplied by a negative number?

It should always flip to the opposite direction. Signup and view all the answers

When solving the inequality \[\frac{3x + 1}{2} \geq 4\, what is the first step to isolate x?

Multiply both sides by 2. Signup and view all the answers

Which of the following inequalities can be solved using the same methods as linear equations?

[2 - x \geq 3] Signup and view all the answers

In the expression \[\frac{4}{3}x - 6 < 7x + 2\, which operation will help isolate x after initial simplification?

Subtracting 4/3x from both sides. Signup and view all the answers

What can be concluded if an inequality leads to a true statement such as [4 < 5]?

The inequality has infinitely many solutions. Signup and view all the answers

Using the multiplication of exponents, what is the result of simplifying the expression $a^5 \times a^{-3}$?

$a^{2}$ Signup and view all the answers

What is the simplified form of the expression $(\frac{3}{4})^{-2}$?

$\frac{16}{9}$ Signup and view all the answers

After applying the power of a power property, what is the simplified expression for $(a^2)^3$?

$a^6$ Signup and view all the answers

What is the correct application of the zero exponent law for the expression $b^0$?

$1$ Signup and view all the answers

Which of the following represents the correct result of applying the division law of exponents to simplify $a^{10}/a^{4}$?

$a^6$ Signup and view all the answers

What will be the result of simplifying the expression $\left(\frac{2a}{3b}\right)^{2}$?

$\frac{4a^2}{9b^2}$ Signup and view all the answers

Applying the prime factorization method, how can the expression $a^4b^2c$ be rewritten?

$(ab^2)(a^2)$ Signup and view all the answers

What is the result of the expression $\frac{a^5b^3}{a^2b^2}$ when simplified?

$a^3b$ Signup and view all the answers

When solving a quadratic equation by factorisation, what is the correct first step?

Rewrite the equation in standard form Signup and view all the answers

In solving simultaneous equations using the elimination method, which action is taken first?

Add or subtract the equations to eliminate a variable Signup and view all the answers

What is the main goal when solving word problems using algebra?

To write equations that represent a mathematical model of the situation Signup and view all the answers

What is a crucial step to take when solving simultaneous equations graphically?

Determine the point of intersection of the graphs Signup and view all the answers

What is typically true about the variables in a literal equation?

They can include multiple variables and constants Signup and view all the answers

During the factorisation of a quadratic equation, what form should the expression be turned into?

A product of linear factors Signup and view all the answers

What operation must be performed to each side of a literal equation to isolate a variable?

Perform the same operation consistently Signup and view all the answers

What must be ensured for a quadratic equation before applying the factorisation method?

The equation should be of the form $ax^2 + bx + c = 0$ Signup and view all the answers

Which method can be utilized to solve systems of equations without manipulating the equations algebraically?

Graphical method Signup and view all the answers

What is the result of simplifying the expression $a^{3/4} \times a^{5/6}$ using the laws of exponents?

$a^{19/24}$ Signup and view all the answers

When rewriting the expression $\left(\frac{a}{b}\right)^{3/4}$, what is the corresponding fractional exponent representation?

$\frac{a^{3/4}}{b^{3/4}}$ Signup and view all the answers

What is the value of $x$ in the equation $2^{2x} = 8$?

$1$ Signup and view all the answers

Which of the following represents the correct application of the power of a power property when simplifying $\left(a^{2/3}\right)^{4/5}$?

$a^{8/15}$ Signup and view all the answers

In solving the equation $3^{2x} = 27$, what method is most suitable?

Equating exponents Signup and view all the answers

How can the expression $\frac{(xy)^{3/2}}{x^{1/2}y^{1/2}}$ be simplified?

$x^{1/2}y^{1}$ Signup and view all the answers

Which expression correctly simplifies according to the laws of exponents?

$a^{m/n + p/q}$ Signup and view all the answers

Which of the following scenarios represents a quadratic equation?

$x^2 - 5x + 6 = 0$ Signup and view all the answers

What is the highest exponent of the variable in an effective quadratic equation?

$2$ Signup and view all the answers

Which step is essential for checking the solution of an equation?

Verification in the original equation Signup and view all the answers

When solving the inequality $2 - x \geq 3$, what is the first step to isolate x?

Subtract 2 from both sides. Signup and view all the answers

In the inequality $\frac{3x + 1}{2} \geq 4$, which operation must be performed to eliminate the fraction?

Multiply both sides by 2. Signup and view all the answers

What must be done to the inequality sign when dividing both sides of $8 > 6$ by -2?

Switch the sign to $\ ext{<}$. Signup and view all the answers

What type of inequality does the expression $\frac{4}{3}x - 6 < 7x + 2$ represent?

Linear inequality with multiple terms on both sides. Signup and view all the answers

What is a potential outcome if an inequality simplifies to a statement like $6 < 2$?

The inequality has no solution. Signup and view all the answers

What is the primary purpose of rewriting a quadratic equation in the form $ax^2 + bx + c = 0$?

To prepare it for factorisation. Signup and view all the answers

Which of the following accurately describes the elimination method for solving simultaneous equations?

It requires making the coefficients of one variable equal and then eliminating it. Signup and view all the answers

When solving word problems, which initial step is the most critical?

Read the question thoroughly to understand the requirements. Signup and view all the answers

In what way can literal equations be effectively solved?

By isolating the unknown variable and then manipulating the equation appropriately. Signup and view all the answers

What do you need to ensure when solving a quadratic equation through factorisation?

The equation must remain balanced after each operation. Signup and view all the answers

When applying substitution in simultaneous equations, which stage follows after expressing one variable in terms of the other?

Use the newly formed expression in the second equation. Signup and view all the answers

Which graphical representation best defines the solution to simultaneous equations?

The coordinates of the point where the two graphs intersect. Signup and view all the answers

In the context of word problems, what does assigning a variable primarily achieve?

It transforms qualitative information into a quantitative format. Signup and view all the answers

What is a vital consideration when rearranging literal equations?

The unknown variable must be isolated through inverse operations. Signup and view all the answers

What is the outcome of applying the power of a power rule to the expression $\left(a^{2/3}\right)^{4/5}$?

$a^{8/15}$ Signup and view all the answers

When simplifying the expression $\frac{a^{3/4}}{a^{1/2}}$, what is the resulting exponent of $a$?

$a^{1/4}$ Signup and view all the answers

Which equation can be solved by equating exponents if $4^{x+1} = 16^{2-x}$?

$4^{x+1} = 4^{4-2x}$ Signup and view all the answers

If $\frac{(x+2)^{1/3}}{(x-3)^{1/4}} = 1$, what condition must $x$ satisfy?

$(x + 2)^{4} = (x - 3)^{3}$ Signup and view all the answers

What is the key property of logarithms used to solve the equation $5^{2x} = 25^{x-1}$?

Logarithms facilitate exponent isolation Signup and view all the answers

What is the correct simplification of the expression $\frac{(ab)^{2}}{a^{1}b^{3}}$?

$a^{1}b^{-1}$ Signup and view all the answers

What is the maximum number of solutions for a quadratic equation?

2 Signup and view all the answers

Which operation should be performed to both sides when isolating the variable $x$ in the equation $2^{x} = 8$?

Take the logarithm of both sides Signup and view all the answers

If $x^{2} + 5x + 6 = 0$, how can this quadratic equation be solved?

By factoring $(x+3)(x+2) = 0$ Signup and view all the answers

What is a valid reason for using the method of substitution when solving simultaneous equations?

To eliminate one variable in an equation Signup and view all the answers

What is the result of simplifying the expression $a^5 imes a^{-2}$?

$a^{3}$ Signup and view all the answers

How should the expression $a^2b^3 imes a^3b^{-1}$ be simplified?

$a^{5}b^{2}$ Signup and view all the answers

What is the result of applying the power of a power property to the expression $(a^2)^3$?

$a^6$ Signup and view all the answers

Which of the following correctly applies the division law of exponents to the expression $rac{b^4}{b^2}$?

$b^{2}$ Signup and view all the answers

How can the expression $rac{(3x^2y)^3}{3^2x^3y^3}$ be simplified?

$3x^{-1}y^{-1}$ Signup and view all the answers

What does the expression $(rac{a^2}{b^3})^4$ simplify to?

$rac{a^{8}}{b^{12}}$ Signup and view all the answers

Which of the following represents the correct application of the zero exponent law for the expression $c^0$?

$1$ Signup and view all the answers

What is the simplified form of the expression $a^{-2} imes a^5$?

$a^{3}$ Signup and view all the answers

Gr 10 Math Ch 2 SUM: Exponents, Equations and Inequalities

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Questions and Answers

What must be done to both sides of a linear inequality when dividing by a negative number?

What is the first step to take when the unknown variable is in the denominator of the equation?

Which of the following is a valid linear inequality?

In the inequality $ rac{4}{3}x - 6 < 7x + 2$, what is the initial operation needed to isolate x?

What can be concluded if an inequality simplifies to a false statement, such as 6 < 2?

What is the result of simplifying the expression $a^3 imes a^4$?

What is the simplified form of $ rac{a^5}{a^2}$?

According to the laws of exponents, what is $(xy)^3$ equal to?

What is the value of $a^0$ when $a eq 0$?

What is $a^{-3}$ equal to?

How do you simplify the expression $ rac{(ab)^2}{(a^2b^2)}$?

What does the expression $( rac{a}{b})^2$ become?

What is the greatest common factor (GCF) of the expression $a^4 + a^3$?

What is the first step for solving a quadratic equation?

In the factorisation method for solving quadratic equations, what is the purpose of setting each factor equal to zero?

When solving simultaneous equations by substitution, what is the first step?

What is a necessary condition for solving simultaneous equations?

Which method involves adding or subtracting two equations to eliminate a variable?

What step is NOT part of solving word problems using algebra?

What does a literal equation represent?

Which operation should be performed to isolate an unknown variable in a literal equation?

What is the graphical solution to simultaneous equations?

What is the last step in the process of solving quadratic equations?

What is the result of multiplying $a^{2/3}$ by $a^{4/5}$?

How would you simplify $ rac{a^{3/4}}{a^{5/6}}$?

Which of the following is the correct application of the power of a power property?

What is the value of $x$ in the equation $2^x = 32$?

When solving the exponential equation $3^x = 81$, which method would best apply?

What is the highest exponent of the variable in a linear equation?

What is a possible scenario in a quadratic equation?

Which step is NOT part of solving a linear equation?

In what condition can logarithms be used to solve exponential equations?

What is the result of simplifying $(xy)^{1/2}$?

What is the first step when solving a quadratic equation using factorisation?

Which method involves expressing one variable in terms of the other?

What ensures that a quadratic equation is balanced during manipulation?

In solving simultaneous equations graphically, what does the solution represent?

What is one way to check the correctness of a solution to a quadratic equation?

When solving a literal equation, what should you do to isolate the unknown variable?

Which statement best describes simultaneous equations?

What is a key consideration when writing equations to solve word problems?

In the elimination method for solving simultaneous equations, what is the goal?

What must you remember when isolating a variable by taking a square root?

Which expression correctly simplifies according to the laws of exponents?

What is the result of applying the negative exponent law to the expression $a^{-3}$?

Which of the following represents the correct application of the division law of exponents?

When simplifying the expression $(ab)^4$, what is the resulting form?

How can the expression $\frac{(xy)^3}{x^2 y^3}$ be simplified?

What is the simplified form of the expression [\frac{6a^4b^2}{3a^2b}]?

Which expression represents the difference of squares correctly?

What is the significance of applying the zero exponent law?

What is the correct expression for raising a product to a power according to the laws of rational exponents?

Which method is used to solve exponential equations when the bases cannot be made the same?

What does the equation $a^{m/n} imes a^{p/q}$ simplify to based on the multiplication of exponents rule?

What must be done first to solve a linear equation?

When can it be concluded that $x = y$ in the context of exponential equations?

How many solutions can a quadratic equation typically have?

In the power of a power property, how is $(a^{m/n})^{p/q}$ expressed?

What operation should be performed to isolate the variable when solving a linear equation?

To simplify a rational exponent such as $ rac{a^{3/4}}{a^{5/6}}$, what should be done with the exponents?

What must be done first when solving the inequality $ rac{3x + 1}{2} geq 4$?

Which inequality correctly represents the result of dividing both sides of $8 > 6$ by -2?

In the inequality $2 - x geq 3$, what is the correct first operation to isolate $x$?

When manipulating the inequality $ rac{4}{3}x - 6 < 7x + 2$, what initial step is required?

What is the correct interpretation if an equation like $6 < 2$ results from solving a linear inequality?

What must be done to both sides when solving the inequality $2 - x \geq 3$?

When a linear inequality such as $\frac{3x + 1}{2} \geq 4$ is presented, what is the first step to solve it?

In solving the inequality $\frac{4}{3}x - 6 < 7x + 2$, what should be done first to isolate x?

What is true about the operation performed on both sides of the inequality when dividing by a negative number?

For the inequality $8 > 6$, what happens if both sides are divided by -2?

What does the expression $a^{-n}$ equal to?

When simplifying the expression $a^5 imes a^2$, what is the result?

To simplify $( rac{3}{2})^3$, which law of exponents should be applied?

What is the simplified result of the expression $ rac{a^4 imes a^3}{a^5}$?

Which expression correctly applies the law of exponents to simplify $(a^2b^3)^2$?

What is the outcome when simplifying the expression $ rac{(ab)^4}{a^2b^3}$?

In the inequality $rac{4}{3}x - 6 < 7x + 2$, what is the initial operation needed to isolate x?

What is the simplified form of $rac{a^5}{a^2}$?

How do you simplify the expression $rac{(ab)^2}{(a^2b^2)}$?

What does the expression $(rac{a}{b})^2$ become?

How would you simplify $rac{a^{3/4}}{a^{5/6}}$?

What must be done first when solving the inequality $rac{3x + 1}{2} geq 4$?

When manipulating the inequality $rac{4}{3}x - 6 < 7x + 2$, what initial step is required?

To simplify $(rac{3}{2})^3$, which law of exponents should be applied?

What is the simplified result of the expression $rac{a^4 imes a^3}{a^5}$?

What is the outcome when simplifying the expression $rac{(ab)^4}{a^2b^3}$?

What is the result when the expression $(rac{2}{3})^{1/2}$ is simplified?

Which of the following shows the correct method for simplifying the expression $rac{a^{5/6}}{a^{1/3}}$?