Simplify sixth root of 8x^15y^3z^3

$\sqrt[6]{8 x^{15} y^{3} z^{3}}$

Step 1

Rewrite $8 x^{15} y^{3} z^{3}$ as ${(x^{2})}^{6} \cdot (8 x^{3} y^{3} z^{3})$ .

Factor out $x^{12}$ .

$\sqrt[6]{8 (x^{12} x^{3}) y^{3} z^{3}}$

Rewrite $x^{12}$ as ${(x^{2})}^{6}$ .

$\sqrt[6]{8 ({(x^{2})}^{6} x^{3}) y^{3} z^{3}}$

Reorder $8$ and ${(x^{2})}^{6}$ .

$\sqrt[6]{{(x^{2})}^{6} \cdot 8 x^{3} y^{3} z^{3}}$

Add parentheses.

$\sqrt[6]{{(x^{2})}^{6} \cdot 8 x^{3} (y^{3} z^{3})}$

Add parentheses.

$\sqrt[6]{{(x^{2})}^{6} \cdot 8 (x^{3} (y^{3} z^{3}))}$

Add parentheses.

$\sqrt[6]{{(x^{2})}^{6} \cdot (8 x^{3} y^{3} z^{3})}$

Step 2

Pull terms out from under the radical.

$x^{2} \sqrt[6]{8 x^{3} y^{3} z^{3}}$

Step 3

Rewrite $8 x^{3} y^{3} z^{3}$ as ${(2 x y z)}^{3}$ .

$x^{2} \sqrt[6]{{(2 x y z)}^{3}}$

Step 4

Rewrite $\sqrt[6]{{(2 x y z)}^{3}}$ as $\sqrt{\sqrt[3]{{(2 x y z)}^{3}}}$ .

$x^{2} \sqrt{\sqrt[3]{{(2 x y z)}^{3}}}$

Step 5

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

$x^{2} \sqrt{2 x y z}$