Question

Select the equivalent expression

Answer 1

Given:

The given expression is $\left(3^{3} \cdot 6^{6}\right)^{-3}$

We need to determine the equivalent expression.

Equivalent expression:

The equivalent expression can be determined by solving the given expression.

Let us apply the exponent rule, $a^{-b}=\frac{1}{a^{b}}$

Thus, we get;

$\frac{1}{\left(3^{3} \cdot 6^{6}\right)^{3}}$

Again, applying the exponent rule, $(a \cdot b)^{n}=a^{n} b^{n}$

Thus, we have;

$\frac{1}{\left(3^{3})^3 \cdot (6^{6}\right)^{3}}$

Simplifying, we get;

$\frac{1}{3^{9} \cdot 6^{18}}$

Thus, the equivalent expression is $\frac{1}{3^{9} \cdot 6^{18}}$

Hence, Option C is the correct answer.