Algebra Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

Add $- 6$ and $18$ .

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

Step 2

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

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

Step 3

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

$z^{3}$