Solve by Factoring x^(1/3)=-5

$x^{\frac{1}{3}} = - 5$

Step 1

Add $5$ to both sides of the equation.

$x^{\frac{1}{3}} + 5 = 0$

Step 2

Subtract $5$ from both sides of the equation.

$x^{\frac{1}{3}} = - 5$

Step 3

Raise each side of the equation to the power of $3$ to eliminate the fractional exponent on the left side.

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

Step 4

Simplify the exponent.

Simplify the left side.

Simplify ${(x^{\frac{1}{3}})}^{3}$ .

Multiply the exponents in ${(x^{\frac{1}{3}})}^{3}$ .

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

$x^{1} = {(- 5)}^{3}$

Simplify.

$x = {(- 5)}^{3}$

Simplify the right side.

Raise $- 5$ to the power of $3$ .

$x = - 125$