91Ó°ÊÓ

We are given an expression ${(-125)}^{\frac{1}{3}}$.

We need to simplify the expression.

The expression ${(-125)}^{\frac{1}{3}}$can be written as a cube root as

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

Rewriting $-125$as a perfect cube and simplifying we get

$\begin{array}{rcl}\sqrt[3]{-125}& =& \sqrt[3]{{(-5)}^3}\\ & =& -5\end{array}$

We are given an expression ${-125}^{\frac{1}{3}}$.

We need to simplify the expression.

The exponent in the expression ${-125}^{\frac{1}{3}}$only applies to the number $125$.

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

The expression $-\left({125}^{\frac{1}{3}}\right)$can be written as a cube root as

$-\left({125}^{\frac{1}{3}}\right)=-\sqrt[3]{125}$

Rewriting $125$as a perfect cube and simplifying we get

$\begin{array}{rcl}-\sqrt[3]{125}& =& -\sqrt[3]{5^3}\\ & =& -5\end{array}$

We are given an expression ${\left(125\right)}^{-\frac{1}{3}}$.

We need to simplify the expression.

Using the negative exponent rule the expression ${\left(125\right)}^{-\frac{1}{3}}$can be written as

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

The expression $\frac{1}{{125}^{{\displaystyle \frac{1}{3}}}}$can be written as a cube root as

$\frac{1}{{125}^{{\displaystyle \frac{1}{3}}}}=\frac{1}{\sqrt[3]{125}}$

Rewriting $125$as a perfect cube and simplifying we get

role="math" localid="1653587225627" $\begin{array}{rcl}\frac{1}{\sqrt[3]{125}}& =& \frac{1}{\sqrt[3]{5^3}}\\ & =& \frac{1}{5}\end{array}$