Solve for x (5+8x)^(1/3)=-3

${(5 + 8 x)}^{\frac{1}{3}} = - 3$

Step 1

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

${({(5 + 8 x)}^{\frac{1}{3}})}^{3} = {(- 3)}^{3}$

Step 2

Simplify the exponent.

Simplify the left side.

Simplify ${({(5 + 8 x)}^{\frac{1}{3}})}^{3}$ .

Multiply the exponents in ${({(5 + 8 x)}^{\frac{1}{3}})}^{3}$ .

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

${(5 + 8 x)}^{\frac{1}{3} \cdot 3} = {(- 3)}^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(5 + 8 x)}^{\frac{1}{3} \cdot 3} = {(- 3)}^{3}$

Rewrite the expression.

${(5 + 8 x)}^{1} = {(- 3)}^{3}$

Simplify.

$5 + 8 x = {(- 3)}^{3}$

Simplify the right side.

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

$5 + 8 x = - 27$

Step 3

Solve for $x$ .

Move all terms not containing $x$ to the right side of the equation.

Subtract $5$ from both sides of the equation.

$8 x = - 27 - 5$

Subtract $5$ from $- 27$ .

$8 x = - 32$

Divide each term in $8 x = - 32$ by $8$ and simplify.

Divide each term in $8 x = - 32$ by $8$ .

$\frac{8 x}{8} = \frac{- 32}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 x}{8} = \frac{- 32}{8}$

Divide $x$ by $1$ .

$x = \frac{- 32}{8}$

Simplify the right side.

Divide $- 32$ by $8$ .

$x = - 4$