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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)

Select the equivalent expression. $\newline$ $(9^{6}\cdot7^{-9})^{-4}=$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{9^{24}}{7^{36}}$ $\newline$ (B) $\frac{7^{36}}{9^{24}}$ $\newline$ (C) $9^{24}\cdot7^{-36}$

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Evaluate expressions using properties of exponents

Full solution

Q. Select the equivalent expression.

\newline

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

?

\newline

Choose

1

answer:

\newline

(A)

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

\newline

(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) $(7^{36})/(9^{24})$ .

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