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 for $\left(3^{-8} \cdot 7^{3}\right)^{-2}$, we first simplify the base by multiplying the exponents of 3 and 7. ‖ ‖ step 2 ⋮ We apply the power of a product rule: $(a \cdot b)^n = a^n \cdot b^n$. So, $\left(3^{-8} \cdot 7^{3}\right)^{-2} = 3^{-8 \cdot -2} \cdot 7^{3 \cdot -2}$. ‖ ‖ step 3 ⋮ Simplifying the exponents, we get $3^{16} \cdot 7^{-6}$. ‖ ***C*** ∻Key Concept∻ ⚹Power of a Product Rule⚹ ∻Explanation∻ ⚹When raising a product to a power, you can apply the exponent to each factor individually.⚹◊What is the rule for raising a power to another power in terms of exponents?⍭ Generate me a similar question◊

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