Algebra Examples

$\frac{\sqrt[4]{8} \cdot \sqrt[4]{16}}{\sqrt[8]{2} \cdot \sqrt[8]{3}}$

Step 1

Simplify the numerator.

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Step 1.1

Combine using the product rule for radicals.

$\frac{\sqrt[4]{8 \cdot 16}}{\sqrt[8]{2} \cdot \sqrt[8]{3}}$

Step 1.2

Multiply $8$ by $16$ .

$\frac{\sqrt[4]{128}}{\sqrt[8]{2} \cdot \sqrt[8]{3}}$

Step 2

Simplify the denominator.

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Step 2.1

Combine using the product rule for radicals.

$\frac{\sqrt[4]{128}}{\sqrt[8]{2 \cdot 3}}$

Step 2.2

Multiply $2$ by $3$ .

$\frac{\sqrt[4]{128}}{\sqrt[8]{6}}$

Step 3

Simplify the numerator.

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Step 3.1

Rewrite $128$ as $2^{4} \cdot 8$ .

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Step 3.1.1

Factor $16$ out of $128$ .

$\frac{\sqrt[4]{16 (8)}}{\sqrt[8]{6}}$

Step 3.1.2

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

$\frac{\sqrt[4]{2^{4} \cdot 8}}{\sqrt[8]{6}}$

Step 3.2

Pull terms out from under the radical.

$\frac{2 \sqrt[4]{8}}{\sqrt[8]{6}}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{2 \sqrt[4]{8}}{\sqrt[8]{6}}$

Decimal Form:

$2.68864576 \dots$