Question

Math

Posted 4 months ago

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

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Answer from Sia

Posted 4 months ago

Solution by Steps

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.

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