Select the equivalent expression.
$$
\left(3^{3} \cdot 6^{6}\right)^{-3}=?
$$

Choose 1 answer:
(A) $\frac{6^{18}}{3^{9}}$
(B) $\frac{3^{9}}{6^{18}}$
(c) $\frac{1}{3^{9} \cdot 6^{18}}$

Question

Select the equivalent expression.
$$
\left(3^{3} \cdot 6^{6}\right)^{-3}=?
$$

Choose 1 answer:
(A) $\frac{6^{18}}{3^{9}}$
(B) $\frac{3^{9}}{6^{18}}$
(c) $\frac{1}{3^{9} \cdot 6^{18}}$

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ We start with the given expression: $\left(3^{3} \cdot 6^{6}\right)^{-3}$ ‖ ‖ step 2 ⋮ Apply the negative exponent rule: $\left(3^{3} \cdot 6^{6}\right)^{-3} = \frac{1}{\left(3^{3} \cdot 6^{6}\right)^{3}}$ ‖ ‖ step 3 ⋮ Simplify the exponent: $\left(3^{3} \cdot 6^{6}\right)^{3} = 3^{3 \cdot 3} \cdot 6^{6 \cdot 3} = 3^{9} \cdot 6^{18}$ ‖ ‖ step 4 ⋮ Combine the results: $\frac{1}{3^{9} \cdot 6^{18}}$ ‖ ***C*** ∻Key Concept∻ ⚹Negative Exponent Rule⚹ ∻Explanation∻ ⚹When an expression with a product is raised to a negative exponent, it is equivalent to the reciprocal of the expression raised to the positive exponent.⚹◊What is the equivalent expression of $\left(3^{3} \cdot 6^{6}\right)^{-3}$?⍭ Generate me a similar question◊

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