Pre-Algebra Examples

$x^{7} - 5 = - 8$

Step 1

Move all terms not containing $x$ to the right side of the equation.

Tap for more steps...

Step 1.1

Add $5$ to both sides of the equation.

$x^{7} = - 8 + 5$

Step 1.2

Add $- 8$ and $5$ .

$x^{7} = - 3$

Step 2

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

$x = \sqrt[7]{- 3}$

Step 3

Simplify $\sqrt[7]{- 3}$ .

Tap for more steps...

Step 3.1

Rewrite $- 3$ as ${(- 1)}^{7} \cdot 3$ .

Tap for more steps...

Step 3.1.1

Rewrite $- 3$ as $- 1 (3)$ .

$x = \sqrt[7]{- 1 (3)}$

Step 3.1.2

Rewrite $- 1$ as ${(- 1)}^{7}$ .

$x = \sqrt[7]{{(- 1)}^{7} \cdot 3}$

Step 3.2

Pull terms out from under the radical.

$x = - 1 \sqrt[7]{3}$

Step 3.3

Rewrite $- 1 \sqrt[7]{3}$ as $- \sqrt[7]{3}$ .

$x = - \sqrt[7]{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - \sqrt[7]{3}$

Decimal Form:

$x = - 1.16993081 \dots$