Algebra Examples

$\frac{\sqrt[3]{54}}{\sqrt[6]{4}}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $54$ as $3^{3} \cdot 2$ .

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Step 1.1.1

Factor $27$ out of $54$ .

$\frac{\sqrt[3]{27 (2)}}{\sqrt[6]{4}}$

Step 1.1.2

Rewrite $27$ as $3^{3}$ .

$\frac{\sqrt[3]{3^{3} \cdot 2}}{\sqrt[6]{4}}$

Step 1.2

Pull terms out from under the radical.

$\frac{3 \sqrt[3]{2}}{\sqrt[6]{4}}$

Step 2

Simplify the denominator.

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Step 2.1

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

$\frac{3 \sqrt[3]{2}}{\sqrt[6]{2^{2}}}$

Step 2.2

Rewrite $\sqrt[6]{2^{2}}$ as $\sqrt[3]{\sqrt{2^{2}}}$ .

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

Step 2.3

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

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

Step 3

Cancel the common factor of $\sqrt[3]{2}$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Divide $3$ by $1$ .

$3$