Algebra Examples

$\sqrt[4]{10^{2} a^{18}}$

Step 1

Raise $10$ to the power of $2$ .

$\sqrt[4]{100 a^{18}}$

Step 2

Rewrite $100 a^{18}$ as ${(a^{4})}^{4} \cdot (100 a^{2})$ .

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Step 2.1

Factor out $a^{16}$ .

$\sqrt[4]{100 (a^{16} a^{2})}$

Step 2.2

Rewrite $a^{16}$ as ${(a^{4})}^{4}$ .

$\sqrt[4]{100 ({(a^{4})}^{4} a^{2})}$

Step 2.3

Reorder $100$ and ${(a^{4})}^{4}$ .

$\sqrt[4]{{(a^{4})}^{4} \cdot 100 a^{2}}$

Step 2.4

Add parentheses.

$\sqrt[4]{{(a^{4})}^{4} \cdot (100 a^{2})}$

Step 3

Pull terms out from under the radical.

$a^{4} \sqrt[4]{100 a^{2}}$

Step 4

Rewrite $100 a^{2}$ as ${(10 a)}^{2}$ .

$a^{4} \sqrt[4]{{(10 a)}^{2}}$

Step 5

Rewrite $\sqrt[4]{{(10 a)}^{2}}$ as $\sqrt{\sqrt{{(10 a)}^{2}}}$ .

$a^{4} \sqrt{\sqrt{{(10 a)}^{2}}}$

Step 6

Pull terms out from under the radical, assuming positive real numbers.

$a^{4} \sqrt{10 a}$