Gr 10 Math Ch 2: Exponent Laws

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What is the result of simplifying the expression $a^5 imes a^3$?

$a^{15}$

$a^8$ (correct)

$a^{5-3}$

$a^2$

What does the expression $\frac{a^7}{a^2}$ simplify to?

$a^{9}$

$a^5$ (correct)

$a^4$

$a^{7-2}$

Which of the following expressions is equivalent to $(xy)^3$?

$x^3y^3$ (correct)

$xy^3$

$x^{3y}$

$x^3y^2$

What is the value of $a^0$ when $a$ is any non-zero number?

1 Signup and view all the answers

Which of these is the correct application of the negative exponent law?

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

Which statement about simplifying $(\frac{a}{b})^2$ is true?

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

How can the expression $a^4b^3/a^2b^1$ be simplified?

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

Which method is NOT typically used to simplify exponential expressions?

Increasing the exponents Signup and view all the answers

What is the result of simplifying $(a^3b^2)^2$ using the exponent laws?

a^6b^4 Signup and view all the answers

Which expression correctly represents the application of the negative exponent law?

a^{-5} = rac{1}{a^5} Signup and view all the answers

When applying the law of division of exponents, what does $rac{a^m}{a^3}$ simplify to?

a^{m-3} Signup and view all the answers

How would you simplify the expression $a^5 imes a^{-2}$?

a^{3} Signup and view all the answers

What is the correct result of this expression: $(rac{2}{3})^2$?

$rac{4}{9}$ Signup and view all the answers

Which of the following represents the factorization of $a^2 - b^2$?

(a - b)(a + b) Signup and view all the answers

How do you simplify a complex fraction such as $rac{a^5}{b^2} imes rac{b^3}{a^2}$?

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

Which of the following statements correctly applies the zero exponent law?

a^{0} = 1 Signup and view all the answers

What expression does the law of raising a product to a power state for two numbers a and b?

(ab)^n = a^n b^n Signup and view all the answers

How should the expression $a^4 imes a^{-5}$ be simplified using the law of exponents?

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

If a and b are positive real numbers, which expression correctly represents the application of the quotient of exponents rule?

$rac{a^m}{b^n} = a^{m-n}$ Signup and view all the answers

Which statement correctly represents the negative exponent law?

$a^{-m} = rac{1}{a^{m}}$ Signup and view all the answers

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

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

What will be the result of simplifying the expression $rac{(ab)^2}{a^3b^2}$?

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

Which of the following expressions illustrates the law of zero exponent correctly?

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

When simplifying the expression $a^5b^2/a^3b^1$, which method should you apply?

Cancel out common factors Signup and view all the answers

What is the result of applying the law of raising a power to a power on the expression $(a^3)^4$?

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

Which law of exponents allows you to simplify the expression $(rac{a^2}{b^3})^3$?

Raising a Quotient to a Power Signup and view all the answers

When simplifying an expression like $a^5 imes a^{-3}$, which step correctly applies exponent laws?

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

In the exponent expression $a^{-2} imes a^4$, what is the final simplified form?

$a^2$ Signup and view all the answers

Which of the following is the result of applying the zero exponent law to the expression $b^0$?

$1$ Signup and view all the answers

What is the result of simplifying the expression $rac{(ab)^2}{a^2b^4}$?

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

Given the expression $a^3(a^{-1}b^2)$, what is the simplified result?