Simplify fifth root of 50t^22

$\sqrt[5]{50 t^{22}}$

Step 1

Rewrite $50 t^{22}$ as ${(t^{4})}^{5} \cdot (50 t^{2})$ .

Factor out $t^{20}$ .

$\sqrt[5]{50 (t^{20} t^{2})}$

Rewrite $t^{20}$ as ${(t^{4})}^{5}$ .

$\sqrt[5]{50 ({(t^{4})}^{5} t^{2})}$

Reorder $50$ and ${(t^{4})}^{5}$ .

$\sqrt[5]{{(t^{4})}^{5} \cdot 50 t^{2}}$

Add parentheses.

$\sqrt[5]{{(t^{4})}^{5} \cdot (50 t^{2})}$

Step 2

Pull terms out from under the radical.

$t^{4} \sqrt[5]{50 t^{2}}$