Simplify cube root of 192x^15y^29

$\sqrt[3]{192 x^{15} y^{29}}$

Step 1

Rewrite $192 x^{15} y^{29}$ as ${(4 x^{5} y^{9})}^{3} \cdot (3 y^{2})$ .

Factor $64$ out of $192$ .

$\sqrt[3]{64 (3) x^{15} y^{29}}$

Rewrite $64$ as $4^{3}$ .

$\sqrt[3]{4^{3} \cdot 3 x^{15} y^{29}}$

Rewrite $x^{15}$ as ${(x^{5})}^{3}$ .

$\sqrt[3]{4^{3} \cdot 3 {(x^{5})}^{3} y^{29}}$

Factor out $y^{27}$ .

$\sqrt[3]{4^{3} \cdot 3 {(x^{5})}^{3} (y^{27} y^{2})}$

Rewrite $y^{27}$ as ${(y^{9})}^{3}$ .

$\sqrt[3]{4^{3} \cdot 3 {(x^{5})}^{3} ({(y^{9})}^{3} y^{2})}$

Move $3$ .

$\sqrt[3]{4^{3} {(x^{5})}^{3} {(y^{9})}^{3} \cdot 3 y^{2}}$

Rewrite $4^{3} {(x^{5})}^{3} {(y^{9})}^{3}$ as ${(4 x^{5} y^{9})}^{3}$ .

$\sqrt[3]{{(4 x^{5} y^{9})}^{3} \cdot 3 y^{2}}$

Add parentheses.

$\sqrt[3]{{(4 x^{5} y^{9})}^{3} \cdot (3 y^{2})}$

Step 2

Pull terms out from under the radical.

$4 x^{5} y^{9} \sqrt[3]{3 y^{2}}$