Simplify fifth root of 243x^6z^13

$\sqrt[5]{243 x^{6} z^{13}}$

Rewrite $243 x^{6} z^{13}$ as ${(3 x z^{2})}^{5} (x z^{3})$ .

Rewrite $243$ as $3^{5}$ .

$\sqrt[5]{3^{5} x^{6} z^{13}}$

Factor out $x^{5}$ .

$\sqrt[5]{3^{5} (x^{5} x) z^{13}}$

Factor out $z^{10}$ .

$\sqrt[5]{3^{5} (x^{5} x) (z^{10} z^{3})}$

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

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

Move $x$ .

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

Rewrite $3^{5} (x^{5}) {(z^{2})}^{5}$ as ${(3 x z^{2})}^{5}$ .

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

Add parentheses.

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

Pull terms out from under the radical.

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