Simplify the Radical Expression cube root of a/b

$\sqrt[3]{\frac{a}{b}}$

Rewrite $\sqrt[3]{\frac{a}{b}}$ as $\frac{\sqrt[3]{a}}{\sqrt[3]{b}}$ .

$\frac{\sqrt[3]{a}}{\sqrt[3]{b}}$

Multiply $\frac{\sqrt[3]{a}}{\sqrt[3]{b}}$ by $\frac{{\sqrt[3]{b}}^{2}}{{\sqrt[3]{b}}^{2}}$ .

$\frac{\sqrt[3]{a}}{\sqrt[3]{b}} \cdot \frac{{\sqrt[3]{b}}^{2}}{{\sqrt[3]{b}}^{2}}$

Combine and simplify the denominator.

Multiply $\frac{\sqrt[3]{a}}{\sqrt[3]{b}}$ by $\frac{{\sqrt[3]{b}}^{2}}{{\sqrt[3]{b}}^{2}}$ .

$\frac{\sqrt[3]{a} {\sqrt[3]{b}}^{2}}{\sqrt[3]{b} {\sqrt[3]{b}}^{2}}$

Raise $\sqrt[3]{b}$ to the power of $1$ .

$\frac{\sqrt[3]{a} {\sqrt[3]{b}}^{2}}{{\sqrt[3]{b}}^{1} {\sqrt[3]{b}}^{2}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{\sqrt[3]{a} {\sqrt[3]{b}}^{2}}{{\sqrt[3]{b}}^{1 + 2}}$

Add $1$ and $2$ .

$\frac{\sqrt[3]{a} {\sqrt[3]{b}}^{2}}{{\sqrt[3]{b}}^{3}}$

Rewrite ${\sqrt[3]{b}}^{3}$ as $b$ .

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

$\frac{\sqrt[3]{a} {\sqrt[3]{b}}^{2}}{{(b^{\frac{1}{3}})}^{3}}$

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

$\frac{\sqrt[3]{a} {\sqrt[3]{b}}^{2}}{b^{\frac{1}{3} \cdot 3}}$

Combine $\frac{1}{3}$ and $3$ .

$\frac{\sqrt[3]{a} {\sqrt[3]{b}}^{2}}{b^{\frac{3}{3}}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{\sqrt[3]{a} {\sqrt[3]{b}}^{2}}{b^{\frac{3}{3}}}$

Rewrite the expression.

$\frac{\sqrt[3]{a} {\sqrt[3]{b}}^{2}}{b^{1}}$

Simplify.

$\frac{\sqrt[3]{a} {\sqrt[3]{b}}^{2}}{b}$

Rewrite ${\sqrt[3]{b}}^{2}$ as ${(b^{2})}^{\frac{1}{3}}$ .

$\frac{\sqrt[3]{a} \sqrt[3]{b^{2}}}{b}$

Combine using the product rule for radicals.

$\frac{\sqrt[3]{a b^{2}}}{b}$