Solve for m cube root of m=3

$\sqrt[3]{m} = 3$

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

${\sqrt[3]{m}}^{3} = 3^{3}$

Simplify each side of the equation.

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

${(m^{\frac{1}{3}})}^{3} = 3^{3}$

Simplify the left side.

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

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

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

$m^{\frac{1}{3} \cdot 3} = 3^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

$m^{\frac{1}{3} \cdot 3} = 3^{3}$

Rewrite the expression.

$m^{1} = 3^{3}$

Simplify.

$m = 3^{3}$

Simplify the right side.

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

$m = 27$