Algebra Examples

$\frac{{(x^{\frac{1}{4}})}^{8}}{\sqrt[3]{x^{3}}}$

Step 1

Multiply the exponents in ${(x^{\frac{1}{4}})}^{8}$ .

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Step 1.1

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

$\frac{x^{\frac{1}{4} \cdot 8}}{\sqrt[3]{x^{3}}}$

Step 1.2

Cancel the common factor of $4$ .

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Step 1.2.1

Factor $4$ out of $8$ .

$\frac{x^{\frac{1}{4} \cdot (4 (2))}}{\sqrt[3]{x^{3}}}$

Step 1.2.2

Cancel the common factor.

$\frac{x^{\frac{1}{4} \cdot (4 \cdot 2)}}{\sqrt[3]{x^{3}}}$

Step 1.2.3

Rewrite the expression.

$\frac{x^{2}}{\sqrt[3]{x^{3}}}$

Step 2

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

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

Step 3

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

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Step 3.1

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

$\frac{x \cdot x}{x}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

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

Step 3.2.2

Factor $x$ out of $x^{1}$ .

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

Step 3.2.3

Cancel the common factor.

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

Step 3.2.4

Rewrite the expression.

$\frac{x}{1}$

Step 3.2.5

Divide $x$ by $1$ .

$x$