Algebra Examples

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

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[8]{8^{3}}$ as $8^{\frac{3}{8}}$ .

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

Step 2

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[8]{8^{4}}$ as $8^{\frac{4}{8}}$ .

$8^{\frac{3}{8}} \cdot 8^{\frac{4}{8}}$

Step 3

Cancel the common factor of $4$ and $8$ .

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Step 3.1

Factor $4$ out of $4$ .

$8^{\frac{3}{8}} \cdot 8^{\frac{4 (1)}{8}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $4$ out of $8$ .

$8^{\frac{3}{8}} \cdot 8^{\frac{4 \cdot 1}{4 \cdot 2}}$

Step 3.2.2

Cancel the common factor.

$8^{\frac{3}{8}} \cdot 8^{\frac{4 \cdot 1}{4 \cdot 2}}$

Step 3.2.3

Rewrite the expression.

$8^{\frac{3}{8}} \cdot 8^{\frac{1}{2}}$