Question

question

simplify: \\((125)^{-\frac{1}{3}}\\).

provide your answer below:

Explanation:

Apply negative exponent rule

$$ (125)^{-\frac{1}{3}} = \frac{1}{(125)^{\frac{1}{3}}} $$

Rewrite base as a power of a prime

$$ 125 = 5^3 \implies \frac{1}{(5^3)^{\frac{1}{3}}} $$

Simplify the exponent

$$ \frac{1}{5^{3 \cdot \frac{1}{3}}} = \frac{1}{5^1} = \frac{1}{5} $$

Answer:

Simplify: \((125)^{-\frac{1}{3}}\).

Provide your answer below:
<blank>\(\frac{1}{5}\)</blank>