Select the equivalent expression. (9^(6)*7^(-9))^(-4)=? Choose 1 answer: (A) (9^(24))/(7^(36)) (B) (7^(36))/(9^(24)) (C) 9^(24)*7^(-36)

Apply product rule: Apply the power of a product rule, which states that (ab)^n = a^n * b^n, to the expression (9^(6)*7^(-9))^(-4). (9^(6)*7^(-9))^(-4) = 9^(6*(-4)) * 7^(-9*(-4))Multiply exponents: Multiply the exponents inside the parentheses by the exponent outside the parentheses. 9^(6*(-4)) * 7^(-9*(-4)) = 9^(-24) * 7^(36)Reciprocal of 9^24: Recognize that 9^(-24) is the reciprocal of 9^(24), which can be written as 1/(9^(24)). 9^(-24) * 7^(36) = (1/(9^(24))) * 7^(36)Rearrange expression: Rearrange the expression to show the division by 9^(24). (1/(9^(24))) * 7^(36) = 7^(36) / 9^(24)Final expression: Match the final expression with the given choices. 7^(36) / 9^(24) corresponds to choice (B) (7^(36))/(9^(24)).

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Math Problems

Grade 8

Evaluate expressions using properties of exponents

Full solution

Q. Select the equivalent expression.

\newline

(9^{6}\cdot7^{-9})^{-4}=

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Choose

1

answer:

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(A)

\frac{9^{24}}{7^{36}}

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(B)

\frac{7^{36}}{9^{24}}

\newline

(C)

9^{24}\cdot7^{-36}

Apply product rule: Apply the power of a product rule, which states that $(ab)^n = a^n \times b^n$ , to the expression $(9^{6}\times7^{-9})^{-4}$ . $\newline$ $(9^{6}\times7^{-9})^{-4} = 9^{6\times(-4)} \times 7^{-9\times(-4)}$
Multiply exponents: Multiply the exponents inside the parentheses by the exponent outside the parentheses. $\newline$ $9^{(6*(-4))} \times 7^{(-9*(-4))} = 9^{-24} \times 7^{36}$
Reciprocal of $9^{24}$ : Recognize that $9^{-24}$ is the reciprocal of $9^{24}$ , which can be written as $\frac{1}{9^{24}}$ . $\newline$ $9^{-24} \times 7^{36} = \left(\frac{1}{9^{24}}\right) \times 7^{36}$
Rearrange expression: Rearrange the expression to show the division by $9^{24}$ . $\newline$ $\left(\frac{1}{9^{24}}\right) \cdot 7^{36} = \frac{7^{36}}{9^{24}}$
Final expression: Match the final expression with the given choices. $\newline$ $7^{36} / 9^{24}$ corresponds to choice (B) $(7^{36})/(9^{24})$ .