Pre-Algebra Examples

$\frac{\sqrt[4]{a b^{4}}}{\sqrt[4]{a^{2} b^{4}}}$

Step 1

Combine $\sqrt[4]{a b^{4}}$ and $\sqrt[4]{a^{2} b^{4}}$ into a single radical.

$\sqrt[4]{\frac{a b^{4}}{a^{2} b^{4}}}$

Step 2

Reduce the expression $\frac{a b^{4}}{a^{2} b^{4}}$ by cancelling the common factors.

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Step 2.1

Factor $a$ out of $a b^{4}$ .

$\sqrt[4]{\frac{a (b^{4})}{a^{2} b^{4}}}$

Step 2.2

Factor $a$ out of $a^{2} b^{4}$ .

$\sqrt[4]{\frac{a (b^{4})}{a (a b^{4})}}$

Step 2.3

Cancel the common factor.

$\sqrt[4]{\frac{a b^{4}}{a (a b^{4})}}$

Step 2.4

Rewrite the expression.

$\sqrt[4]{\frac{b^{4}}{a b^{4}}}$

Step 3

Cancel the common factor of $b^{4}$ .

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Step 3.1

Cancel the common factor.

$\sqrt[4]{\frac{b^{4}}{a b^{4}}}$

Step 3.2

Rewrite the expression.

$\sqrt[4]{\frac{1}{a}}$

Step 4

Rewrite $\sqrt[4]{\frac{1}{a}}$ as $\frac{\sqrt[4]{1}}{\sqrt[4]{a}}$ .

$\frac{\sqrt[4]{1}}{\sqrt[4]{a}}$

Step 5

Any root of $1$ is $1$ .

$\frac{1}{\sqrt[4]{a}}$

Step 6

Multiply $\frac{1}{\sqrt[4]{a}}$ by $\frac{{\sqrt[4]{a}}^{3}}{{\sqrt[4]{a}}^{3}}$ .

$\frac{1}{\sqrt[4]{a}} \cdot \frac{{\sqrt[4]{a}}^{3}}{{\sqrt[4]{a}}^{3}}$

Step 7

Combine and simplify the denominator.

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Step 7.1

Multiply $\frac{1}{\sqrt[4]{a}}$ by $\frac{{\sqrt[4]{a}}^{3}}{{\sqrt[4]{a}}^{3}}$ .

$\frac{{\sqrt[4]{a}}^{3}}{\sqrt[4]{a} {\sqrt[4]{a}}^{3}}$

Step 7.2

Raise $\sqrt[4]{a}$ to the power of $1$ .

$\frac{{\sqrt[4]{a}}^{3}}{{\sqrt[4]{a}}^{1} {\sqrt[4]{a}}^{3}}$

Step 7.3

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

$\frac{{\sqrt[4]{a}}^{3}}{{\sqrt[4]{a}}^{1 + 3}}$

Step 7.4

Add $1$ and $3$ .

$\frac{{\sqrt[4]{a}}^{3}}{{\sqrt[4]{a}}^{4}}$

Step 7.5

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

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Step 7.5.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{a}$ as $a^{\frac{1}{4}}$ .

$\frac{{\sqrt[4]{a}}^{3}}{{(a^{\frac{1}{4}})}^{4}}$

Step 7.5.2

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

$\frac{{\sqrt[4]{a}}^{3}}{a^{\frac{1}{4} \cdot 4}}$

Step 7.5.3

Combine $\frac{1}{4}$ and $4$ .

$\frac{{\sqrt[4]{a}}^{3}}{a^{\frac{4}{4}}}$

Step 7.5.4

Cancel the common factor of $4$ .

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Step 7.5.4.1

Cancel the common factor.

$\frac{{\sqrt[4]{a}}^{3}}{a^{\frac{4}{4}}}$

Step 7.5.4.2

Rewrite the expression.

$\frac{{\sqrt[4]{a}}^{3}}{a^{1}}$

Step 7.5.5

Simplify.

$\frac{{\sqrt[4]{a}}^{3}}{a}$

Step 8

Rewrite ${\sqrt[4]{a}}^{3}$ as $\sqrt[4]{a^{3}}$ .

$\frac{\sqrt[4]{a^{3}}}{a}$