Finite Math Examples

$\sqrt[5]{- b^{14} c^{30}}$

Step 1

Rewrite $- b^{14} c^{30}$ as ${(- b^{2} c^{6})}^{5} b^{4}$ .

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Step 1.1

Rewrite $- 1$ as ${(- 1)}^{5}$ .

$\sqrt[5]{{(- 1)}^{5} b^{14} c^{30}}$

Step 1.2

Factor out $b^{10}$ .

$\sqrt[5]{{(- 1)}^{5} (b^{10} b^{4}) c^{30}}$

Step 1.3

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

$\sqrt[5]{{(- 1)}^{5} ({(b^{2})}^{5} b^{4}) c^{30}}$

Step 1.4

Rewrite $c^{30}$ as ${(c^{6})}^{5}$ .

$\sqrt[5]{{(- 1)}^{5} ({(b^{2})}^{5} b^{4}) {(c^{6})}^{5}}$

Step 1.5

Move $b^{4}$ .

$\sqrt[5]{{(- 1)}^{5} ({(b^{2})}^{5}) {(c^{6})}^{5} b^{4}}$

Step 1.6

Rewrite ${(- 1)}^{5} ({(b^{2})}^{5}) {(c^{6})}^{5}$ as ${(- b^{2} c^{6})}^{5}$ .

$\sqrt[5]{{(- b^{2} c^{6})}^{5} b^{4}}$

Step 2

Pull terms out from under the radical.

$- b^{2} c^{6} \sqrt[5]{b^{4}}$