Simplify 20 root of a^10b^15c^30

$\sqrt[20]{a^{10} b^{15} c^{30}}$

Rewrite $a^{10} b^{15} c^{30}$ as $c^{20} (a^{10} b^{15} c^{10})$ .

Factor out $c^{20}$ .

$\sqrt[20]{a^{10} b^{15} (c^{20} c^{10})}$

Move $b^{15}$ .

$\sqrt[20]{a^{10} c^{20} b^{15} c^{10}}$

Reorder $a^{10}$ and $c^{20}$ .

$\sqrt[20]{c^{20} a^{10} b^{15} c^{10}}$

Add parentheses.

$\sqrt[20]{c^{20} a^{10} (b^{15} c^{10})}$

Add parentheses.

$\sqrt[20]{c^{20} (a^{10} b^{15} c^{10})}$

Pull terms out from under the radical.

$c \sqrt[20]{a^{10} b^{15} c^{10}}$

Rewrite $a^{10} b^{15} c^{10}$ as ${(a^{2} b^{3} c^{2})}^{5}$ .

$c \sqrt[20]{{(a^{2} b^{3} c^{2})}^{5}}$

Rewrite $\sqrt[20]{{(a^{2} b^{3} c^{2})}^{5}}$ as $\sqrt[4]{\sqrt[5]{{(a^{2} b^{3} c^{2})}^{5}}}$ .

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

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

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