Simplify ( cube root of x)/( cube root of xy)

$\frac{\sqrt[3]{x}}{\sqrt[3]{x y}}$

Combine $\sqrt[3]{x}$ and $\sqrt[3]{x y}$ into a single radical.

$\sqrt[3]{\frac{x}{x y}}$

Reduce the expression $\frac{x}{x y}$ by cancelling the common factors.

Cancel the common factor.

$\sqrt[3]{\frac{x}{x y}}$

Rewrite the expression.

$\sqrt[3]{\frac{1}{y}}$

Rewrite $\sqrt[3]{\frac{1}{y}}$ as $\frac{\sqrt[3]{1}}{\sqrt[3]{y}}$ .

$\frac{\sqrt[3]{1}}{\sqrt[3]{y}}$

Any root of $1$ is $1$ .

$\frac{1}{\sqrt[3]{y}}$

Multiply $\frac{1}{\sqrt[3]{y}}$ by $\frac{{\sqrt[3]{y}}^{2}}{{\sqrt[3]{y}}^{2}}$ .

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

Combine and simplify the denominator.

Multiply $\frac{1}{\sqrt[3]{y}}$ by $\frac{{\sqrt[3]{y}}^{2}}{{\sqrt[3]{y}}^{2}}$ .

$\frac{{\sqrt[3]{y}}^{2}}{\sqrt[3]{y} {\sqrt[3]{y}}^{2}}$

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

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

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

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

Add $1$ and $2$ .

$\frac{{\sqrt[3]{y}}^{2}}{{\sqrt[3]{y}}^{3}}$

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

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

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

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

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

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

$\frac{{\sqrt[3]{y}}^{2}}{y^{\frac{3}{3}}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{{\sqrt[3]{y}}^{2}}{y^{\frac{3}{3}}}$

Rewrite the expression.

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

Simplify.

$\frac{{\sqrt[3]{y}}^{2}}{y}$

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

$\frac{\sqrt[3]{y^{2}}}{y}$