Algebra Examples

${(\sqrt[3]{41})}^{9}$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{41}$ as $41^{\frac{1}{3}}$ .

${(41^{\frac{1}{3}})}^{9}$

Step 2

Multiply the exponents in ${(41^{\frac{1}{3}})}^{9}$ .

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Step 2.1

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

$41^{\frac{1}{3} \cdot 9}$

Step 2.2

Cancel the common factor of $3$ .

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Step 2.2.1

Factor $3$ out of $9$ .

$41^{\frac{1}{3} \cdot (3 (3))}$

Step 2.2.2

Cancel the common factor.

$41^{\frac{1}{3} \cdot (3 \cdot 3)}$

Step 2.2.3

Rewrite the expression.

$41^{3}$