Select the equivalent expression.
$$
\left(3^{-8} \cdot 7^{3}\right)^{-2}=?
$$

Choose 1 answer:
(A) $21^{10}$
(B) $\frac{7^{6}}{3^{16}}$
(c) $3^{16} \cdot 7^{-6}$

Question

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

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To find the equivalent expression, we start by considering the given expression $\left(3^{-8} \cdot 7^{3}\right)^{-2}$. ‖ ‖ step 2 ⋮ We apply the power of a product rule, which states that $(ab)^n = a^n \cdot b^n$, to get $\left(3^{-8}\right)^{-2} \cdot \left(7^{3}\right)^{-2}$. ‖ ‖ step 3 ⋮ Next, we apply the power of a power rule, which states that $(a^m)^n = a^{mn}$, to simplify the expression to $3^{16} \cdot 7^{-6}$. ‖ ‖ step 4 ⋮ The simplified expression is $3^{16} \cdot 7^{-6}$, which matches one of the answer choices. ‖ ***C*** ∻Key Concept∻ ⚹Exponent Rules⚹ ∻Explanation∻ ⚹When simplifying expressions with exponents, we use the power of a product rule and the power of a power rule to find the equivalent expression.⚹◊What is the rule for simplifying expressions with negative exponents?⍭ Generate me a similar question◊

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