Algebra Examples

$\frac{\sqrt[4]{5}}{\sqrt{5}}$

Multiply $\frac{\sqrt[4]{5}}{\sqrt{5}}$ by $\frac{\sqrt{5}}{\sqrt{5}}$ .

$\frac{\sqrt[4]{5}}{\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}}$

Combine and simplify the denominator.

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Multiply $\frac{\sqrt[4]{5}}{\sqrt{5}}$ by $\frac{\sqrt{5}}{\sqrt{5}}$ .

$\frac{\sqrt[4]{5} \sqrt{5}}{\sqrt{5} \sqrt{5}}$

Raise $\sqrt{5}$ to the power of $1$ .

$\frac{\sqrt[4]{5} \sqrt{5}}{{\sqrt{5}}^{1} \sqrt{5}}$

Raise $\sqrt{5}$ to the power of $1$ .

$\frac{\sqrt[4]{5} \sqrt{5}}{{\sqrt{5}}^{1} {\sqrt{5}}^{1}}$

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

$\frac{\sqrt[4]{5} \sqrt{5}}{{\sqrt{5}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{\sqrt[4]{5} \sqrt{5}}{{\sqrt{5}}^{2}}$

Rewrite ${\sqrt{5}}^{2}$ as $5$ .

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Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5}$ as $5^{\frac{1}{2}}$ .

$\frac{\sqrt[4]{5} \sqrt{5}}{{(5^{\frac{1}{2}})}^{2}}$

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

$\frac{\sqrt[4]{5} \sqrt{5}}{5^{\frac{1}{2} \cdot 2}}$

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

$\frac{\sqrt[4]{5} \sqrt{5}}{5^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$\frac{\sqrt[4]{5} \sqrt{5}}{5^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{\sqrt[4]{5} \sqrt{5}}{5^{1}}$

Evaluate the exponent.

$\frac{\sqrt[4]{5} \sqrt{5}}{5}$

Simplify the numerator.

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Rewrite the expression using the least common index of $4$ .

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Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5}$ as $5^{\frac{1}{2}}$ .

$\frac{\sqrt[4]{5} \cdot 5^{\frac{1}{2}}}{5}$

Rewrite $5^{\frac{1}{2}}$ as $5^{\frac{2}{4}}$ .

$\frac{\sqrt[4]{5} \cdot 5^{\frac{2}{4}}}{5}$

Rewrite $5^{\frac{2}{4}}$ as $\sqrt[4]{5^{2}}$ .

$\frac{\sqrt[4]{5} \sqrt[4]{5^{2}}}{5}$

Combine using the product rule for radicals.

$\frac{\sqrt[4]{5 \cdot 5^{2}}}{5}$

Multiply $5$ by $5^{2}$ by adding the exponents.

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Multiply $5$ by $5^{2}$ .

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Raise $5$ to the power of $1$ .

$\frac{\sqrt[4]{5^{1} \cdot 5^{2}}}{5}$

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

$\frac{\sqrt[4]{5^{1 + 2}}}{5}$

Add $1$ and $2$ .

$\frac{\sqrt[4]{5^{3}}}{5}$

Raise $5$ to the power of $3$ .

$\frac{\sqrt[4]{125}}{5}$