Algebra Examples

$\sqrt[4]{144 a^{12} b^{3}}$

Step 1

Rewrite $144 a^{12} b^{3}$ as ${(2 a^{3})}^{4} \cdot (9 b^{3})$ .

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Step 1.1

Factor $16$ out of $144$ .

$\sqrt[4]{16 (9) a^{12} b^{3}}$

Step 1.2

Rewrite $16$ as $2^{4}$ .

$\sqrt[4]{2^{4} \cdot 9 a^{12} b^{3}}$

Step 1.3

Rewrite $a^{12}$ as ${(a^{3})}^{4}$ .

$\sqrt[4]{2^{4} \cdot 9 {(a^{3})}^{4} b^{3}}$

Step 1.4

Move $9$ .

$\sqrt[4]{2^{4} {(a^{3})}^{4} \cdot 9 b^{3}}$

Step 1.5

Rewrite $2^{4} {(a^{3})}^{4}$ as ${(2 a^{3})}^{4}$ .

$\sqrt[4]{{(2 a^{3})}^{4} \cdot 9 b^{3}}$

Step 1.6

Add parentheses.

$\sqrt[4]{{(2 a^{3})}^{4} \cdot (9 b^{3})}$

Step 2

Pull terms out from under the radical.

$2 a^{3} \sqrt[4]{9 b^{3}}$