Solve for c cube root of c=2

$\sqrt[3]{c} = 2$

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

${\sqrt[3]{c}}^{3} = 2^{3}$

Simplify each side of the equation.

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

${(c^{\frac{1}{3}})}^{3} = 2^{3}$

Simplify the left side.

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

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

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

$c^{\frac{1}{3} \cdot 3} = 2^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

$c^{\frac{1}{3} \cdot 3} = 2^{3}$

Rewrite the expression.

$c^{1} = 2^{3}$

Simplify.

$c = 2^{3}$

Simplify the right side.

Raise $2$ to the power of $3$ .

$c = 8$