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Select the equivalent expression. $\newline$ $(3^{-8}\cdot7^{3})^{-2}=$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $\newline$ $\frac{7^{6}}{3^{16}}$ $\newline$ (B) $\newline$ $21^{10}$ $\newline$ (C) $\newline$ $3^{16}\cdot7^{-6}$

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Multiplication with rational exponents

Full solution

Q. Select the equivalent expression.

\newline

(3^{-8}\cdot7^{3})^{-2}=

?

\newline

Choose

1

answer:

\newline

(A)

\newline

\frac{7^{6}}{3^{16}}

\newline

(B)

\newline

21^{10}

\newline

(C)

\newline

3^{16}\cdot7^{-6}

Simplify inside parentheses: Simplify the expression inside the parentheses first. $\newline$ $(3^{-8} \times 7^{3})^{-2}$ $\newline$ Using the property of exponents $(a^{m} \times b^{m}) = (ab)^{m}$ , we get: $\newline$ (3^{-8} \times 7^{3})^{-2} = (3 \times 7)^{-8 \times 3}^{-2}

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