Simplify fourth root of z^-6z^18

$\sqrt[4]{z^{- 6} z^{18}}$

Multiply $z^{- 6}$ by $z^{18}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\sqrt[4]{z^{- 6 + 18}}$

Add $- 6$ and $18$ .

$\sqrt[4]{z^{12}}$

Rewrite $z^{12}$ as ${(z^{3})}^{4}$ .

$\sqrt[4]{{(z^{3})}^{4}}$

Pull terms out from under the radical, assuming positive real numbers.

$z^{3}$