Finite Math Examples

$\sqrt[5]{5 a^{5} b^{9} c^{13}}$

Step 1

Rewrite $5 a^{5} b^{9} c^{13}$ as ${(a b c^{2})}^{5} \cdot (5 b^{4} c^{3})$ .

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Step 1.1

Factor out $b^{5}$ .

$\sqrt[5]{5 a^{5} (b^{5} b^{4}) c^{13}}$

Step 1.2

Factor out $c^{10}$ .

$\sqrt[5]{5 a^{5} (b^{5} b^{4}) (c^{10} c^{3})}$

Step 1.3

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

$\sqrt[5]{5 a^{5} (b^{5} b^{4}) ({(c^{2})}^{5} c^{3})}$

Step 1.4

Move $b^{4}$ .

$\sqrt[5]{5 a^{5} (b^{5}) {(c^{2})}^{5} b^{4} c^{3}}$

Step 1.5

Move $5$ .

$\sqrt[5]{a^{5} (b^{5}) {(c^{2})}^{5} \cdot 5 b^{4} c^{3}}$

Step 1.6

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

$\sqrt[5]{{(a b c^{2})}^{5} \cdot 5 b^{4} c^{3}}$

Step 1.7

Add parentheses.

$\sqrt[5]{{(a b c^{2})}^{5} \cdot 5 (b^{4} c^{3})}$

Step 1.8

Add parentheses.

$\sqrt[5]{{(a b c^{2})}^{5} \cdot (5 b^{4} c^{3})}$

Step 2

Pull terms out from under the radical.

$a b c^{2} \sqrt[5]{5 b^{4} c^{3}}$