Algebra Examples

$\frac{{(x^{10})}^{\frac{1}{5}}}{\sqrt[2]{x^{8}}}$

Step 1

Multiply the exponents in ${(x^{10})}^{\frac{1}{5}}$ .

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Step 1.1

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

$\frac{x^{10 (\frac{1}{5})}}{\sqrt{x^{8}}}$

Step 1.2

Cancel the common factor of $5$ .

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Step 1.2.1

Factor $5$ out of $10$ .

$\frac{x^{5 (2) \frac{1}{5}}}{\sqrt{x^{8}}}$

Step 1.2.2

Cancel the common factor.

$\frac{x^{5 \cdot 2 \frac{1}{5}}}{\sqrt{x^{8}}}$

Step 1.2.3

Rewrite the expression.

$\frac{x^{2}}{\sqrt{x^{8}}}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $x^{8}$ as ${(x^{4})}^{2}$ .

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

Step 2.2

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

$\frac{x^{2}}{x^{4}}$

Step 3

Cancel the common factor of $x^{2}$ and $x^{4}$ .

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Step 3.1

Multiply by $1$ .

$\frac{x^{2} \cdot 1}{x^{4}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $x^{2}$ out of $x^{4}$ .

$\frac{x^{2} \cdot 1}{x^{2} x^{2}}$

Step 3.2.2

Cancel the common factor.

$\frac{x^{2} \cdot 1}{x^{2} x^{2}}$

Step 3.2.3

Rewrite the expression.

$\frac{1}{x^{2}}$