Algebra Examples

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

Step 1

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

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

Step 2

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

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Step 2.1

Cancel the common factor.

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

Step 2.2

Rewrite the expression.

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

Step 3

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

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

Step 4

Any root of $1$ is $1$ .

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

Step 5

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

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

Step 6

Combine and simplify the denominator.

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Step 6.1

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

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

Step 6.2

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

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

Step 6.3

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

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

Step 6.4

Add $1$ and $2$ .

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

Step 6.5

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

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Step 6.5.1

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

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

Step 6.5.2

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

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

Step 6.5.3

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

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

Step 6.5.4

Cancel the common factor of $3$ .

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Step 6.5.4.1

Cancel the common factor.

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

Step 6.5.4.2

Rewrite the expression.

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

Step 6.5.5

Simplify.

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

Step 7

Rewrite ${\sqrt[3]{y}}^{2}$ as $\sqrt[3]{y^{2}}$ .

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