Algebra Examples

$\frac{4 x^{- 4} y^{\frac{2}{3}}}{\sqrt[4]{16 x^{4} y^{2}}}$

Step 1

Move $x^{- 4}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{4 y^{\frac{2}{3}}}{\sqrt[4]{16 x^{4} y^{2}} x^{4}}$

Step 2

Simplify the denominator.

Tap for more steps...

Step 2.1

Rewrite $16 x^{4} y^{2}$ as ${(2 x)}^{4} y^{2}$ .

Tap for more steps...

Step 2.1.1

Rewrite $16$ as $2^{4}$ .

$\frac{4 y^{\frac{2}{3}}}{\sqrt[4]{2^{4} x^{4} y^{2}} x^{4}}$

Step 2.1.2

Rewrite $2^{4} x^{4}$ as ${(2 x)}^{4}$ .

$\frac{4 y^{\frac{2}{3}}}{\sqrt[4]{{(2 x)}^{4} y^{2}} x^{4}}$

Step 2.2

Pull terms out from under the radical.

$\frac{4 y^{\frac{2}{3}}}{2 x \sqrt[4]{y^{2}} x^{4}}$

Step 2.3

Rewrite $\sqrt[4]{y^{2}}$ as $\sqrt{\sqrt{y^{2}}}$ .

$\frac{4 y^{\frac{2}{3}}}{2 x \sqrt{\sqrt{y^{2}}} x^{4}}$

Step 2.4

Pull terms out from under the radical, assuming positive real numbers.

$\frac{4 y^{\frac{2}{3}}}{2 x \sqrt{y} x^{4}}$

Step 2.5

Multiply $x$ by $x^{4}$ by adding the exponents.

Tap for more steps...

Step 2.5.1

Move $x^{4}$ .

$\frac{4 y^{\frac{2}{3}}}{2 (x^{4} x) \sqrt{y}}$

Step 2.5.2

Multiply $x^{4}$ by $x$ .

Tap for more steps...

Step 2.5.2.1

Raise $x$ to the power of $1$ .

$\frac{4 y^{\frac{2}{3}}}{2 (x^{4} x^{1}) \sqrt{y}}$

Step 2.5.2.2

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

$\frac{4 y^{\frac{2}{3}}}{2 x^{4 + 1} \sqrt{y}}$

Step 2.5.3

Add $4$ and $1$ .

$\frac{4 y^{\frac{2}{3}}}{2 x^{5} \sqrt{y}}$

Step 3

Factor $2$ out of $4 y^{\frac{2}{3}}$ .

$\frac{2 (2 y^{\frac{2}{3}})}{2 x^{5} \sqrt{y}}$

Step 4

Cancel the common factors.

Tap for more steps...

Step 4.1

Factor $2$ out of $2 x^{5} \sqrt{y}$ .

$\frac{2 (2 y^{\frac{2}{3}})}{2 (x^{5} \sqrt{y})}$

Step 4.2

Cancel the common factor.

$\frac{2 (2 y^{\frac{2}{3}})}{2 (x^{5} \sqrt{y})}$

Step 4.3

Rewrite the expression.

$\frac{2 y^{\frac{2}{3}}}{x^{5} \sqrt{y}}$

Step 5

Multiply $\frac{2 y^{\frac{2}{3}}}{x^{5} \sqrt{y}}$ by $\frac{\sqrt{y}}{\sqrt{y}}$ .

$\frac{2 y^{\frac{2}{3}}}{x^{5} \sqrt{y}} \cdot \frac{\sqrt{y}}{\sqrt{y}}$

Step 6

Combine and simplify the denominator.

Tap for more steps...

Step 6.1

Multiply $\frac{2 y^{\frac{2}{3}}}{x^{5} \sqrt{y}}$ by $\frac{\sqrt{y}}{\sqrt{y}}$ .

$\frac{2 y^{\frac{2}{3}} \sqrt{y}}{x^{5} \sqrt{y} \sqrt{y}}$

Step 6.2

Move $\sqrt{y}$ .

$\frac{2 y^{\frac{2}{3}} \sqrt{y}}{x^{5} (\sqrt{y} \sqrt{y})}$

Step 6.3

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

$\frac{2 y^{\frac{2}{3}} \sqrt{y}}{x^{5} ({\sqrt{y}}^{1} \sqrt{y})}$

Step 6.4

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

$\frac{2 y^{\frac{2}{3}} \sqrt{y}}{x^{5} ({\sqrt{y}}^{1} {\sqrt{y}}^{1})}$

Step 6.5

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

$\frac{2 y^{\frac{2}{3}} \sqrt{y}}{x^{5} {\sqrt{y}}^{1 + 1}}$

Step 6.6

Add $1$ and $1$ .

$\frac{2 y^{\frac{2}{3}} \sqrt{y}}{x^{5} {\sqrt{y}}^{2}}$

Step 6.7

Rewrite ${\sqrt{y}}^{2}$ as $y$ .

Tap for more steps...

Step 6.7.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{y}$ as $y^{\frac{1}{2}}$ .

$\frac{2 y^{\frac{2}{3}} \sqrt{y}}{x^{5} {(y^{\frac{1}{2}})}^{2}}$

Step 6.7.2

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

$\frac{2 y^{\frac{2}{3}} \sqrt{y}}{x^{5} y^{\frac{1}{2} \cdot 2}}$

Step 6.7.3

Combine $\frac{1}{2}$ and $2$ .

$\frac{2 y^{\frac{2}{3}} \sqrt{y}}{x^{5} y^{\frac{2}{2}}}$

Step 6.7.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 6.7.4.1

Cancel the common factor.

$\frac{2 y^{\frac{2}{3}} \sqrt{y}}{x^{5} y^{\frac{2}{2}}}$

Step 6.7.4.2

Rewrite the expression.

$\frac{2 y^{\frac{2}{3}} \sqrt{y}}{x^{5} y^{1}}$

Step 6.7.5

Simplify.

$\frac{2 y^{\frac{2}{3}} \sqrt{y}}{x^{5} y}$

Step 7

Move $y^{\frac{2}{3}}$ to the denominator using the negative exponent rule $b^{n} = \frac{1}{b^{- n}}$ .

$\frac{2 \sqrt{y}}{x^{5} y \cdot y^{- \frac{2}{3}}}$

Step 8

Multiply $y$ by $y^{- \frac{2}{3}}$ by adding the exponents.

Tap for more steps...

Step 8.1

Move $y^{- \frac{2}{3}}$ .

$\frac{2 \sqrt{y}}{x^{5} (y^{- \frac{2}{3}} y)}$

Step 8.2

Multiply $y^{- \frac{2}{3}}$ by $y$ .

Tap for more steps...

Step 8.2.1

Raise $y$ to the power of $1$ .

$\frac{2 \sqrt{y}}{x^{5} (y^{- \frac{2}{3}} y^{1})}$

Step 8.2.2

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

$\frac{2 \sqrt{y}}{x^{5} y^{- \frac{2}{3} + 1}}$

Step 8.3

Write $1$ as a fraction with a common denominator.

$\frac{2 \sqrt{y}}{x^{5} y^{- \frac{2}{3} + \frac{3}{3}}}$

Step 8.4

Combine the numerators over the common denominator.

$\frac{2 \sqrt{y}}{x^{5} y^{\frac{- 2 + 3}{3}}}$

Step 8.5

Add $- 2$ and $3$ .

$\frac{2 \sqrt{y}}{x^{5} y^{\frac{1}{3}}}$