Find All Complex Solutions x^5=-48

$x^{5} = - 48$

Step 1

Take the 5th root of both sides of the equation to eliminate the exponent on the left side.

$x = \sqrt[5]{- 48}$

Step 2

Simplify $\sqrt[5]{- 48}$ .

Rewrite $- 48$ as ${(- 1)}^{5} \cdot 48$ .

Rewrite $- 48$ as $- 1 (48)$ .

$x = \sqrt[5]{- 1 (48)}$

Rewrite $- 1$ as ${(- 1)}^{5}$ .

$x = \sqrt[5]{{(- 1)}^{5} \cdot 48}$

Pull terms out from under the radical.

$x = - 1 \sqrt[5]{48}$

Rewrite $- 1 \sqrt[5]{48}$ as $- \sqrt[5]{48}$ .

$x = - \sqrt[5]{48}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = - \sqrt[5]{48}$

Decimal Form:

$x = - 2.16894354 \dots$