Simplify cube root of 24x^15y^29

$\sqrt[3]{24 x^{15} y^{29}}$

Step 1

Rewrite $24 x^{15} y^{29}$ as ${(2 x^{5} y^{9})}^{3} \cdot (3 y^{2})$ .

Factor $8$ out of $24$ .

$\sqrt[3]{8 (3) x^{15} y^{29}}$

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

$\sqrt[3]{2^{3} \cdot 3 x^{15} y^{29}}$

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

$\sqrt[3]{2^{3} \cdot 3 {(x^{5})}^{3} y^{29}}$

Factor out $y^{27}$ .

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

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

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

Move $3$ .

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

Rewrite $2^{3} {(x^{5})}^{3} {(y^{9})}^{3}$ as ${(2 x^{5} y^{9})}^{3}$ .

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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