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?
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What can be concluded if an inequality simplifies to a false statement, such as 6 < 2?
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What is the result of simplifying the expression $a^3 imes a^4$?
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What is the simplified form of $rac{a^5}{a^2}$?
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According to the laws of exponents, what is $(xy)^3$ equal to?
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What is the value of $a^0$ when $a eq 0$?
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What is $a^{-3}$ equal to?
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How do you simplify the expression $rac{(ab)^2}{(a^2b^2)}$?
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What does the expression $(rac{a}{b})^2$ become?
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What is the greatest common factor (GCF) of the expression $a^4 + a^3$?
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What is the first step for solving a quadratic equation?
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In the factorisation method for solving quadratic equations, what is the purpose of setting each factor equal to zero?
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When solving simultaneous equations by substitution, what is the first step?
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What is a necessary condition for solving simultaneous equations?
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Which method involves adding or subtracting two equations to eliminate a variable?
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What step is NOT part of solving word problems using algebra?
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What does a literal equation represent?
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Which operation should be performed to isolate an unknown variable in a literal equation?
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What is the graphical solution to simultaneous equations?
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What is the last step in the process of solving quadratic equations?
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What is the result of multiplying $a^{2/3}$ by $a^{4/5}$?
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How would you simplify $rac{a^{3/4}}{a^{5/6}}$?
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Which of the following is the correct application of the power of a power property?
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What is the value of $x$ in the equation $2^x = 32$?
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When solving the exponential equation $3^x = 81$, which method would best apply?
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What is the highest exponent of the variable in a linear equation?
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What is a possible scenario in a quadratic equation?
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Which step is NOT part of solving a linear equation?
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In what condition can logarithms be used to solve exponential equations?
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What is the result of simplifying $(xy)^{1/2}$?
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What is the first step when solving a quadratic equation using factorisation?
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Which method involves expressing one variable in terms of the other?
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What ensures that a quadratic equation is balanced during manipulation?
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In solving simultaneous equations graphically, what does the solution represent?
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What is one way to check the correctness of a solution to a quadratic equation?
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When solving a literal equation, what should you do to isolate the unknown variable?
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Which statement best describes simultaneous equations?
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What is a key consideration when writing equations to solve word problems?
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In the elimination method for solving simultaneous equations, what is the goal?
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What must you remember when isolating a variable by taking a square root?
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Which expression correctly simplifies according to the laws of exponents?
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What is the result of applying the negative exponent law to the expression $a^{-3}$?
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Which of the following represents the correct application of the division law of exponents?
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When simplifying the expression $(ab)^4$, what is the resulting form?
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How can the expression $\frac{(xy)^3}{x^2 y^3}$ be simplified?
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What is the simplified form of the expression [\frac{6a^4b^2}{3a^2b}]?
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Which expression represents the difference of squares correctly?
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What is the significance of applying the zero exponent law?
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What is the correct expression for raising a product to a power according to the laws of rational exponents?
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Which method is used to solve exponential equations when the bases cannot be made the same?
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What does the equation $a^{m/n} imes a^{p/q}$ simplify to based on the multiplication of exponents rule?
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What must be done first to solve a linear equation?
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When can it be concluded that $x = y$ in the context of exponential equations?
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How many solutions can a quadratic equation typically have?
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In the power of a power property, how is $(a^{m/n})^{p/q}$ expressed?
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What operation should be performed to isolate the variable when solving a linear equation?
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To simplify a rational exponent such as $ rac{a^{3/4}}{a^{5/6}}$, what should be done with the exponents?
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What must be done first when solving the inequality $rac{3x + 1}{2} geq 4$?
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Which inequality correctly represents the result of dividing both sides of $8 > 6$ by -2?
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In the inequality $2 - x geq 3$, what is the correct first operation to isolate $x$?
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When manipulating the inequality $rac{4}{3}x - 6 < 7x + 2$, what initial step is required?
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What is the correct interpretation if an equation like $6 < 2$ results from solving a linear inequality?
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What must be done to both sides when solving the inequality $2 - x \geq 3$?
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When a linear inequality such as $\frac{3x + 1}{2} \geq 4$ is presented, what is the first step to solve it?
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In solving the inequality $\frac{4}{3}x - 6 < 7x + 2$, what should be done first to isolate x?
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What is true about the operation performed on both sides of the inequality when dividing by a negative number?
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For the inequality $8 > 6$, what happens if both sides are divided by -2?
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What does the expression $a^{-n}$ equal to?
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When simplifying the expression $a^5 imes a^2$, what is the result?
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To simplify $(rac{3}{2})^3$, which law of exponents should be applied?
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What is the simplified result of the expression $rac{a^4 imes a^3}{a^5}$?
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Which expression correctly applies the law of exponents to simplify $(a^2b^3)^2$?
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What is the outcome when simplifying the expression $rac{(ab)^4}{a^2b^3}$?
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What does the zero exponent law state?
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When applying the law of exponents, what is true about raising a number to a negative exponent?
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How can the expression $a^{1/2} imes a^{3/4}$ be simplified?
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What is the result when the expression $(rac{2}{3})^{1/2}$ is simplified?
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If $2^x = 2^5$, what can be concluded about the variable $x$?
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When solving the equation $3^{x} = 27$, which approach is most useful?
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Which of the following shows the correct method for simplifying the expression $rac{a^{5/6}}{a^{1/3}}$?
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What is the characteristic of a quadratic equation?
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Which of the following options illustrates the power of a power property incorrectly?
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If an exponential equation simplifies to $4 < 2$ after manipulation, what does it indicate?
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Which method should be used to solve the equation $x^2 - 5x + 6 = 0$?
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When solving linear equations, what should be done first?
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What is the correct order of operations when rewriting a quadratic equation for factorisation?
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What does substituting into the second equation achieve when solving simultaneous equations by substitution?
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What must be ensured when performing operations on one side of a quadratic equation?
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What is the main goal of using the elimination method in solving simultaneous equations?
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When solving a literal equation, what is the first action to isolate the unknown variable?
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Which step is NOT part of the problem-solving strategy for word problems?
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What is the graphical solution to simultaneous equations visually represented as?
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Why is checking the solution important after solving a quadratic equation?
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When rearranging a literal equation, what must be considered about the terms containing the unknown variable?
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What role does dividing by common factors play in solving a quadratic equation?
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What must occur to the inequality sign when both sides of a linear inequality are multiplied by a negative number?
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When solving the inequality \[\frac{3x + 1}{2} \geq 4\, what is the first step to isolate x?
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Which of the following inequalities can be solved using the same methods as linear equations?
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In the expression \[\frac{4}{3}x - 6 < 7x + 2\, which operation will help isolate x after initial simplification?
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What can be concluded if an inequality leads to a true statement such as [4 < 5]?
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Using the multiplication of exponents, what is the result of simplifying the expression $a^5 \times a^{-3}$?
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What is the simplified form of the expression $(\frac{3}{4})^{-2}$?
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After applying the power of a power property, what is the simplified expression for $(a^2)^3$?
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What is the correct application of the zero exponent law for the expression $b^0$?
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Which of the following represents the correct result of applying the division law of exponents to simplify $a^{10}/a^{4}$?
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What will be the result of simplifying the expression $\left(\frac{2a}{3b}\right)^{2}$?
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Applying the prime factorization method, how can the expression $a^4b^2c$ be rewritten?
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What is the result of the expression $\frac{a^5b^3}{a^2b^2}$ when simplified?
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When solving a quadratic equation by factorisation, what is the correct first step?
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In solving simultaneous equations using the elimination method, which action is taken first?
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What is the main goal when solving word problems using algebra?
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What is a crucial step to take when solving simultaneous equations graphically?
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What is typically true about the variables in a literal equation?
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During the factorisation of a quadratic equation, what form should the expression be turned into?
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What operation must be performed to each side of a literal equation to isolate a variable?
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What must be ensured for a quadratic equation before applying the factorisation method?
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Which method can be utilized to solve systems of equations without manipulating the equations algebraically?
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What is the result of simplifying the expression $a^{3/4} \times a^{5/6}$ using the laws of exponents?
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When rewriting the expression $\left(\frac{a}{b}\right)^{3/4}$, what is the corresponding fractional exponent representation?
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What is the value of $x$ in the equation $2^{2x} = 8$?
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Which of the following represents the correct application of the power of a power property when simplifying $\left(a^{2/3}\right)^{4/5}$?
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In solving the equation $3^{2x} = 27$, what method is most suitable?
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How can the expression $\frac{(xy)^{3/2}}{x^{1/2}y^{1/2}}$ be simplified?
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Which expression correctly simplifies according to the laws of exponents?
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Which of the following scenarios represents a quadratic equation?
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What is the highest exponent of the variable in an effective quadratic equation?
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Which step is essential for checking the solution of an equation?
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When solving the inequality $2 - x \geq 3$, what is the first step to isolate x?
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In the inequality $\frac{3x + 1}{2} \geq 4$, which operation must be performed to eliminate the fraction?
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What must be done to the inequality sign when dividing both sides of $8 > 6$ by -2?
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What type of inequality does the expression $\frac{4}{3}x - 6 < 7x + 2$ represent?
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What is a potential outcome if an inequality simplifies to a statement like $6 < 2$?
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What is the primary purpose of rewriting a quadratic equation in the form $ax^2 + bx + c = 0$?
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Which of the following accurately describes the elimination method for solving simultaneous equations?
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When solving word problems, which initial step is the most critical?
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In what way can literal equations be effectively solved?
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What do you need to ensure when solving a quadratic equation through factorisation?
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When applying substitution in simultaneous equations, which stage follows after expressing one variable in terms of the other?
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Which graphical representation best defines the solution to simultaneous equations?
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In the context of word problems, what does assigning a variable primarily achieve?
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What is a vital consideration when rearranging literal equations?
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What is the outcome of applying the power of a power rule to the expression $\left(a^{2/3}\right)^{4/5}$?
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When simplifying the expression $\frac{a^{3/4}}{a^{1/2}}$, what is the resulting exponent of $a$?
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Which equation can be solved by equating exponents if $4^{x+1} = 16^{2-x}$?
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If $\frac{(x+2)^{1/3}}{(x-3)^{1/4}} = 1$, what condition must $x$ satisfy?
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What is the key property of logarithms used to solve the equation $5^{2x} = 25^{x-1}$?
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What is the correct simplification of the expression $\frac{(ab)^{2}}{a^{1}b^{3}}$?
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What is the maximum number of solutions for a quadratic equation?
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Which operation should be performed to both sides when isolating the variable $x$ in the equation $2^{x} = 8$?
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If $x^{2} + 5x + 6 = 0$, how can this quadratic equation be solved?
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What is a valid reason for using the method of substitution when solving simultaneous equations?
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What is the result of simplifying the expression $a^5 imes a^{-2}$?
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How should the expression $a^2b^3 imes a^3b^{-1}$ be simplified?
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What is the result of applying the power of a power property to the expression $(a^2)^3$?
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Which of the following correctly applies the division law of exponents to the expression $rac{b^4}{b^2}$?
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How can the expression $rac{(3x^2y)^3}{3^2x^3y^3}$ be simplified?
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What does the expression $(rac{a^2}{b^3})^4$ simplify to?
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Which of the following represents the correct application of the zero exponent law for the expression $c^0$?
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What is the simplified form of the expression $a^{-2} imes a^5$?
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