Simplify fifth root of a^3s^10d^15f^2

$\sqrt[5]{a^{3} s^{10} d^{15} f^{2}}$

Step 1

Rewrite $a^{3} s^{10} d^{15} f^{2}$ as ${(s^{2} d^{3})}^{5} (a^{3} f^{2})$ .

Rewrite $s^{10}$ as ${(s^{2})}^{5}$ .

$\sqrt[5]{a^{3} {(s^{2})}^{5} d^{15} f^{2}}$

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

$\sqrt[5]{a^{3} {(s^{2})}^{5} {(d^{3})}^{5} f^{2}}$

Move $a^{3}$ .

$\sqrt[5]{{(s^{2})}^{5} {(d^{3})}^{5} a^{3} f^{2}}$

Rewrite ${(s^{2})}^{5} {(d^{3})}^{5}$ as ${(s^{2} d^{3})}^{5}$ .

$\sqrt[5]{{(s^{2} d^{3})}^{5} a^{3} f^{2}}$

Add parentheses.

$\sqrt[5]{{(s^{2} d^{3})}^{5} (a^{3} f^{2})}$

Step 2

Pull terms out from under the radical.

$s^{2} d^{3} \sqrt[5]{a^{3} f^{2}}$