Finite Math Examples

$\frac{\sqrt[5]{243 a^{12}}}{\sqrt[5]{b^{10}}}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $243 a^{12}$ as ${(3 a^{2})}^{5} a^{2}$ .

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Step 1.1.1

Rewrite $243$ as $3^{5}$ .

$\frac{\sqrt[5]{3^{5} a^{12}}}{\sqrt[5]{b^{10}}}$

Step 1.1.2

Factor out $a^{10}$ .

$\frac{\sqrt[5]{3^{5} (a^{10} a^{2})}}{\sqrt[5]{b^{10}}}$

Step 1.1.3

Rewrite $a^{10}$ as ${(a^{2})}^{5}$ .

$\frac{\sqrt[5]{3^{5} ({(a^{2})}^{5} a^{2})}}{\sqrt[5]{b^{10}}}$

Step 1.1.4

Rewrite $3^{5} {(a^{2})}^{5}$ as ${(3 a^{2})}^{5}$ .

$\frac{\sqrt[5]{{(3 a^{2})}^{5} a^{2}}}{\sqrt[5]{b^{10}}}$

Step 1.2

Pull terms out from under the radical.

$\frac{3 a^{2} \sqrt[5]{a^{2}}}{\sqrt[5]{b^{10}}}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $b^{10}$ as ${(b^{2})}^{5}$ .

$\frac{3 a^{2} \sqrt[5]{a^{2}}}{\sqrt[5]{{(b^{2})}^{5}}}$

Step 2.2

Pull terms out from under the radical, assuming real numbers.

$\frac{3 a^{2} \sqrt[5]{a^{2}}}{b^{2}}$