Algebra Examples

$r s^{2} \sqrt[5]{32 r^{4} s^{10}}$

Step 1

Rewrite $32 r^{4} s^{10}$ as ${(2 s^{2})}^{5} r^{4}$ .

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Step 1.1

Rewrite $32$ as $2^{5}$ .

$r s^{2} \sqrt[5]{2^{5} r^{4} s^{10}}$

Step 1.2

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

$r s^{2} \sqrt[5]{2^{5} r^{4} {(s^{2})}^{5}}$

Step 1.3

Move $r^{4}$ .

$r s^{2} \sqrt[5]{2^{5} {(s^{2})}^{5} r^{4}}$

Step 1.4

Rewrite $2^{5} {(s^{2})}^{5}$ as ${(2 s^{2})}^{5}$ .

$r s^{2} \sqrt[5]{{(2 s^{2})}^{5} r^{4}}$

Step 2

Pull terms out from under the radical.

$r s^{2} (2 s^{2} \sqrt[5]{r^{4}})$

Step 3

Rewrite using the commutative property of multiplication.

$2 r s^{2} (s^{2} \sqrt[5]{r^{4}})$

Step 4

Multiply $s^{2}$ by $s^{2}$ by adding the exponents.

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Step 4.1

Move $s^{2}$ .

$2 r (s^{2} s^{2}) \sqrt[5]{r^{4}}$

Step 4.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2 r s^{2 + 2} \sqrt[5]{r^{4}}$

Step 4.3

Add $2$ and $2$ .

$2 r s^{4} \sqrt[5]{r^{4}}$