Algebra Examples

$\sqrt[4]{a^{5}} \div 2 \sqrt[4]{a}$

Step 1

Simplify the numerator.

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Step 1.1

Factor out $a^{4}$ .

$\sqrt[4]{a^{4} a} \div 2 \sqrt[4]{a}$

Step 1.2

Pull terms out from under the radical.

$| a | \sqrt[4]{a} \div 2 \sqrt[4]{a}$

Step 2

Rewrite the division as a fraction.

$\frac{| a | \sqrt[4]{a}}{2} \sqrt[4]{a}$

Step 3

Multiply $\frac{| a | \sqrt[4]{a}}{2} \sqrt[4]{a}$ .

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Step 3.1

Combine $\frac{| a | \sqrt[4]{a}}{2}$ and $\sqrt[4]{a}$ .

$\frac{| a | \sqrt[4]{a} \sqrt[4]{a}}{2}$

Step 3.2

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

$\frac{| a | ({\sqrt[4]{a}}^{1} \sqrt[4]{a})}{2}$

Step 3.3

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

$\frac{| a | ({\sqrt[4]{a}}^{1} {\sqrt[4]{a}}^{1})}{2}$

Step 3.4

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

$\frac{| a | {\sqrt[4]{a}}^{1 + 1}}{2}$

Step 3.5

Add $1$ and $1$ .

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

Step 4

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

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Step 4.1

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

$\frac{| a | {(a^{\frac{1}{4}})}^{2}}{2}$

Step 4.2

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

$\frac{| a | a^{\frac{1}{4} \cdot 2}}{2}$

Step 4.3

Combine $\frac{1}{4}$ and $2$ .

$\frac{| a | a^{\frac{2}{4}}}{2}$

Step 4.4

Cancel the common factor of $2$ and $4$ .

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Step 4.4.1

Factor $2$ out of $2$ .

$\frac{| a | a^{\frac{2 (1)}{4}}}{2}$

Step 4.4.2

Cancel the common factors.

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Step 4.4.2.1

Factor $2$ out of $4$ .

$\frac{| a | a^{\frac{2 \cdot 1}{2 \cdot 2}}}{2}$

Step 4.4.2.2

Cancel the common factor.

$\frac{| a | a^{\frac{2 \cdot 1}{2 \cdot 2}}}{2}$

Step 4.4.2.3

Rewrite the expression.

$\frac{| a | a^{\frac{1}{2}}}{2}$

Step 4.5

Rewrite $a^{\frac{1}{2}}$ as $\sqrt{a}$ .

$\frac{| a | \sqrt{a}}{2}$