Algebra Examples

${(\frac{a^{12}}{b^{6}})}^{\frac{1}{6}}$

Step 1

Apply the product rule to $\frac{a^{12}}{b^{6}}$ .

$\frac{{(a^{12})}^{\frac{1}{6}}}{{(b^{6})}^{\frac{1}{6}}}$

Step 2

Multiply the exponents in ${(a^{12})}^{\frac{1}{6}}$ .

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Step 2.1

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

$\frac{a^{12 (\frac{1}{6})}}{{(b^{6})}^{\frac{1}{6}}}$

Step 2.2

Cancel the common factor of $6$ .

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Step 2.2.1

Factor $6$ out of $12$ .

$\frac{a^{6 (2) \frac{1}{6}}}{{(b^{6})}^{\frac{1}{6}}}$

Step 2.2.2

Cancel the common factor.

$\frac{a^{6 \cdot 2 \frac{1}{6}}}{{(b^{6})}^{\frac{1}{6}}}$

Step 2.2.3

Rewrite the expression.

$\frac{a^{2}}{{(b^{6})}^{\frac{1}{6}}}$

Step 3

Simplify the denominator.

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Step 3.1

Multiply the exponents in ${(b^{6})}^{\frac{1}{6}}$ .

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Step 3.1.1

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

$\frac{a^{2}}{b^{6 (\frac{1}{6})}}$

Step 3.1.2

Cancel the common factor of $6$ .

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Step 3.1.2.1

Cancel the common factor.

$\frac{a^{2}}{b^{6 (\frac{1}{6})}}$

Step 3.1.2.2

Rewrite the expression.

$\frac{a^{2}}{b^{1}}$

Step 3.2

Simplify.

$\frac{a^{2}}{b}$