Simplify ( cube root of 750z^17)/( cube root of 2)

$\frac{\sqrt[3]{750 z^{17}}}{\sqrt[3]{2}}$

Combine $\sqrt[3]{750 z^{17}}$ and $\sqrt[3]{2}$ into a single radical.

$\sqrt[3]{\frac{750 z^{17}}{2}}$

Reduce the expression by cancelling the common factors.

Reduce the expression $\frac{750 z^{17}}{2}$ by cancelling the common factors.

Factor $2$ out of $750 z^{17}$ .

$\sqrt[3]{\frac{2 (375 z^{17})}{2}}$

Factor $2$ out of $2$ .

$\sqrt[3]{\frac{2 (375 z^{17})}{2 (1)}}$

Cancel the common factor.

$\sqrt[3]{\frac{2 (375 z^{17})}{2 \cdot 1}}$

Rewrite the expression.

$\sqrt[3]{\frac{375 z^{17}}{1}}$

Divide $375 z^{17}$ by $1$ .

$\sqrt[3]{375 z^{17}}$

Rewrite $375 z^{17}$ as ${(5 z^{5})}^{3} \cdot (3 z^{2})$ .

Factor $125$ out of $375$ .

$\sqrt[3]{125 (3) z^{17}}$

Rewrite $125$ as $5^{3}$ .

$\sqrt[3]{5^{3} \cdot 3 z^{17}}$

Factor out $z^{15}$ .

$\sqrt[3]{5^{3} \cdot 3 (z^{15} z^{2})}$

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

$\sqrt[3]{5^{3} \cdot 3 ({(z^{5})}^{3} z^{2})}$

Move $3$ .

$\sqrt[3]{5^{3} {(z^{5})}^{3} \cdot 3 z^{2}}$

Rewrite $5^{3} {(z^{5})}^{3}$ as ${(5 z^{5})}^{3}$ .

$\sqrt[3]{{(5 z^{5})}^{3} \cdot 3 z^{2}}$

Add parentheses.

$\sqrt[3]{{(5 z^{5})}^{3} \cdot (3 z^{2})}$

Pull terms out from under the radical.

$5 z^{5} \sqrt[3]{3 z^{2}}$