Simplify fourth root of 10^2a^18

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

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

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

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

Factor out $a^{16}$ .

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

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

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

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

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

Add parentheses.

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

Pull terms out from under the radical.

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

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

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

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

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

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

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