Precalculus Examples

$z^{5} = - 243 i$

Step 1

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$z = \sqrt[5]{- 243 i}$

Step 2

Simplify $\sqrt[5]{- 243 i}$ .

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Step 2.1

Rewrite $- 243$ as ${(- 3)}^{5}$ .

$z = \sqrt[5]{{(- 3)}^{5} i}$

Step 2.2

Pull terms out from under the radical.

$z = - 3 \sqrt[5]{i}$