Simplify cube root of 16a^3b^4c^5d^6e^2

$\sqrt[3]{16 a^{3} b^{4} c^{5} d^{6} e^{2}}$

Rewrite $16 a^{3} b^{4} c^{5} d^{6} e^{2}$ as ${(2 a b c d^{2})}^{3} \cdot (2 b c^{2} e^{2})$ .

Factor $8$ out of $16$ .

$\sqrt[3]{8 (2) a^{3} b^{4} c^{5} d^{6} e^{2}}$

Rewrite $8$ as $2^{3}$ .

$\sqrt[3]{2^{3} \cdot 2 a^{3} b^{4} c^{5} d^{6} e^{2}}$

Factor out $b^{3}$ .

$\sqrt[3]{2^{3} \cdot 2 a^{3} (b^{3} b) c^{5} d^{6} e^{2}}$

Factor out $c^{3}$ .

$\sqrt[3]{2^{3} \cdot 2 a^{3} (b^{3} b) (c^{3} c^{2}) d^{6} e^{2}}$

Rewrite $d^{6}$ as ${(d^{2})}^{3}$ .

$\sqrt[3]{2^{3} \cdot 2 a^{3} (b^{3} b) (c^{3} c^{2}) {(d^{2})}^{3} e^{2}}$

Move $c^{2}$ .

$\sqrt[3]{2^{3} \cdot 2 a^{3} (b^{3} b) (c^{3}) {(d^{2})}^{3} c^{2} e^{2}}$

Move $b$ .

$\sqrt[3]{2^{3} \cdot 2 a^{3} (b^{3}) (c^{3}) {(d^{2})}^{3} b c^{2} e^{2}}$

Move $2$ .

$\sqrt[3]{(2^{3} a^{3} (b^{3})) (c^{3}) {(d^{2})}^{3} \cdot 2 b c^{2} e^{2}}$

Rewrite $((2^{3} a^{3} (b^{3})) (c^{3})) {(d^{2})}^{3}$ as ${(2 a b c d^{2})}^{3}$ .

$\sqrt[3]{{(2 a b c d^{2})}^{3} \cdot 2 b c^{2} e^{2}}$

Add parentheses.

$\sqrt[3]{{(2 a b c d^{2})}^{3} \cdot 2 b (c^{2} e^{2})}$

Add parentheses.

$\sqrt[3]{{(2 a b c d^{2})}^{3} \cdot 2 (b (c^{2} e^{2}))}$

Add parentheses.

$\sqrt[3]{{(2 a b c d^{2})}^{3} \cdot (2 b c^{2} e^{2})}$

Pull terms out from under the radical.

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