Simplify the Radical Expression (-125)^(1/3)

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

Step 1

Rewrite $- 125$ as ${(- 5)}^{3}$ .

${({(- 5)}^{3})}^{\frac{1}{3}}$

Step 2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(- 5)}^{3 (\frac{1}{3})}$

Step 3

Cancel the common factor of $3$ .

Cancel the common factor.

${(- 5)}^{3 (\frac{1}{3})}$

Rewrite the expression.

${(- 5)}^{1}$

Step 4

Evaluate the exponent.

$- 5$