Precalculus Examples

$\frac{\sqrt{16 x^{2} \sqrt{x}}}{\sqrt[4]{81 x^{5}}}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $16 x^{2} \sqrt{x}$ as ${(4 x)}^{2} \sqrt{x}$ .

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Step 1.1.1

Rewrite $16$ as $4^{2}$ .

$\frac{\sqrt{4^{2} x^{2} \sqrt{x}}}{\sqrt[4]{81 x^{5}}}$

Step 1.1.2

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

$\frac{\sqrt{{(4 x)}^{2} \sqrt{x}}}{\sqrt[4]{81 x^{5}}}$

Step 1.2

Pull terms out from under the radical.

$\frac{4 x \sqrt{\sqrt{x}}}{\sqrt[4]{81 x^{5}}}$

Step 1.3

Rewrite $\sqrt{\sqrt{x}}$ as $\sqrt[4]{x}$ .

$\frac{4 x \sqrt[4]{x}}{\sqrt[4]{81 x^{5}}}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $81 x^{5}$ as ${(3 x)}^{4} x$ .

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Step 2.1.1

Rewrite $81$ as $3^{4}$ .

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

Step 2.1.2

Factor out $x^{4}$ .

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

Step 2.1.3

Rewrite $3^{4} x^{4}$ as ${(3 x)}^{4}$ .

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

Step 2.2

Pull terms out from under the radical.

$\frac{4 x \sqrt[4]{x}}{3 x \sqrt[4]{x}}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Cancel the common factor of $x$ .

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Step 3.1.1

Cancel the common factor.

$\frac{4 x \sqrt[4]{x}}{3 x \sqrt[4]{x}}$

Step 3.1.2

Rewrite the expression.

$\frac{4 \sqrt[4]{x}}{3 \sqrt[4]{x}}$

Step 3.2

Cancel the common factor of $\sqrt[4]{x}$ .

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Step 3.2.1

Cancel the common factor.

$\frac{4 \sqrt[4]{x}}{3 \sqrt[4]{x}}$

Step 3.2.2

Rewrite the expression.

$\frac{4}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{4}{3}$

Decimal Form:

$1.\overline{3}$

Mixed Number Form:

$1 \frac{1}{3}$