Simplify sixth root of 125a^3b^9c^6

$\sqrt[6]{125 a^{3} b^{9} c^{6}}$

Step 1

Rewrite $125 a^{3} b^{9} c^{6}$ as ${(b c)}^{6} \cdot (125 a^{3} b^{3})$ .

Factor out $b^{6}$ .

$\sqrt[6]{125 a^{3} (b^{6} b^{3}) c^{6}}$

Move $b^{3}$ .

$\sqrt[6]{125 a^{3} (b^{6}) c^{6} b^{3}}$

Move $a^{3}$ .

$\sqrt[6]{(125 (b^{6})) c^{6} a^{3} b^{3}}$

Move $125$ .

$\sqrt[6]{(b^{6}) c^{6} \cdot 125 a^{3} b^{3}}$

Rewrite $(b^{6}) c^{6}$ as ${(b c)}^{6}$ .

$\sqrt[6]{{(b c)}^{6} \cdot 125 a^{3} b^{3}}$

Add parentheses.

$\sqrt[6]{{(b c)}^{6} \cdot 125 (a^{3} b^{3})}$

Add parentheses.

$\sqrt[6]{{(b c)}^{6} \cdot (125 a^{3} b^{3})}$

Step 2

Pull terms out from under the radical.

$b c \sqrt[6]{125 a^{3} b^{3}}$

Step 3

Rewrite $125 a^{3} b^{3}$ as ${(5 a b)}^{3}$ .

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

Step 4

Rewrite $\sqrt[6]{{(5 a b)}^{3}}$ as $\sqrt{\sqrt[3]{{(5 a b)}^{3}}}$ .

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

Step 5

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

$b c \sqrt{5 a b}$