Algebra Examples

${(\sqrt[3]{3})}^{6}$

Step 1

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

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Step 1.1

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

${(3^{\frac{1}{3}})}^{6}$

Step 1.2

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

$3^{\frac{1}{3} \cdot 6}$

Step 1.3

Combine $\frac{1}{3}$ and $6$ .

$3^{\frac{6}{3}}$

Step 1.4

Cancel the common factor of $6$ and $3$ .

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Step 1.4.1

Factor $3$ out of $6$ .

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

Step 1.4.2

Cancel the common factors.

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Step 1.4.2.1

Factor $3$ out of $3$ .

$3^{\frac{3 \cdot 2}{3 (1)}}$

Step 1.4.2.2

Cancel the common factor.

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

Step 1.4.2.3

Rewrite the expression.

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

Step 1.4.2.4

Divide $2$ by $1$ .

$3^{2}$

Step 2

Raise $3$ to the power of $2$ .

$9$