Algebra Examples

$\sqrt[5]{x^{4}} \cdot \sqrt[5]{x^{4}}$

Step 1

Multiply $\sqrt[5]{x^{4}} \sqrt[5]{x^{4}}$ .

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Step 1.1

Raise $\sqrt[5]{x^{4}}$ to the power of $1$ .

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

Step 1.2

Raise $\sqrt[5]{x^{4}}$ to the power of $1$ .

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

Step 1.3

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

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

Step 1.4

Add $1$ and $1$ .

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

Step 2

Rewrite ${\sqrt[5]{x^{4}}}^{2}$ as $\sqrt[5]{{(x^{4})}^{2}}$ .

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

Step 3

Apply basic rules of exponents.

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Step 3.1

Multiply the exponents in ${(x^{4})}^{2}$ .

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Step 3.1.1

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

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

Step 3.1.2

Multiply $4$ by $2$ .

$\sqrt[5]{x^{8}}$

Step 3.2

Factor out $x^{5}$ .

$\sqrt[5]{x^{5} x^{3}}$

Step 4

Pull terms out from under the radical.

$x \sqrt[5]{x^{3}}$