Basic Math Examples

$\sqrt[5]{- 1024 a^{30} b^{31}}$

Step 1

Rewrite $- 1024 a^{30} b^{31}$ as ${(- 4 a^{6} b^{6})}^{5} b$ .

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Step 1.1

Rewrite $- 1024$ as ${(- 4)}^{5}$ .

$\sqrt[5]{{(- 4)}^{5} a^{30} b^{31}}$

Step 1.2

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

$\sqrt[5]{{(- 4)}^{5} {(a^{6})}^{5} b^{31}}$

Step 1.3

Factor out $b^{30}$ .

$\sqrt[5]{{(- 4)}^{5} {(a^{6})}^{5} (b^{30} b)}$

Step 1.4

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

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

Step 1.5

Rewrite ${(- 4)}^{5} {(a^{6})}^{5} {(b^{6})}^{5}$ as ${(- 4 a^{6} b^{6})}^{5}$ .

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

Step 2

Pull terms out from under the radical.

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