Simplify seventh root of 75t^30

$\sqrt[7]{75 t^{30}}$

Step 1

Rewrite $75 t^{30}$ as ${(t^{4})}^{7} \cdot (75 t^{2})$ .

Factor out $t^{28}$ .

$\sqrt[7]{75 (t^{28} t^{2})}$

Rewrite $t^{28}$ as ${(t^{4})}^{7}$ .

$\sqrt[7]{75 ({(t^{4})}^{7} t^{2})}$

Reorder $75$ and ${(t^{4})}^{7}$ .

$\sqrt[7]{{(t^{4})}^{7} \cdot 75 t^{2}}$

Add parentheses.

$\sqrt[7]{{(t^{4})}^{7} \cdot (75 t^{2})}$

Step 2

Pull terms out from under the radical.

$t^{4} \sqrt[7]{75 t^{2}}$