Solve for a 4 = cube root of 8a

$4 = \sqrt[3]{8 a}$

Rewrite the equation as $\sqrt[3]{8 a} = 4$ .

$\sqrt[3]{8 a} = 4$

To remove the radical on the left side of the equation, cube both sides of the equation.

${\sqrt[3]{8 a}}^{3} = 4^{3}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{8 a}$ as ${(8 a)}^{\frac{1}{3}}$ .

${({(8 a)}^{\frac{1}{3}})}^{3} = 4^{3}$

Simplify the left side.

Simplify ${({(8 a)}^{\frac{1}{3}})}^{3}$ .

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

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

${(8 a)}^{\frac{1}{3} \cdot 3} = 4^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(8 a)}^{\frac{1}{3} \cdot 3} = 4^{3}$

Rewrite the expression.

${(8 a)}^{1} = 4^{3}$

Simplify.

$8 a = 4^{3}$

Simplify the right side.

Raise $4$ to the power of $3$ .

$8 a = 64$

Divide each term in $8 a = 64$ by $8$ and simplify.

Divide each term in $8 a = 64$ by $8$ .

$\frac{8 a}{8} = \frac{64}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 a}{8} = \frac{64}{8}$

Divide $a$ by $1$ .

$a = \frac{64}{8}$

Simplify the right side.

Divide $64$ by $8$ .

$a = 8$