Solve for x x^4=64

$x^{4} = 64$

Step 1

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

$x = \pm \sqrt[4]{64}$

Step 2

Simplify $\pm \sqrt[4]{64}$ .

Rewrite $64$ as $2^{4} \cdot 4$ .

Factor $16$ out of $64$ .

$x = \pm \sqrt[4]{16 (4)}$

Rewrite $16$ as $2^{4}$ .

$x = \pm \sqrt[4]{2^{4} \cdot 4}$

Pull terms out from under the radical.

$x = \pm 2 \sqrt[4]{4}$

Rewrite $4$ as $2^{2}$ .

$x = \pm 2 \sqrt[4]{2^{2}}$

Rewrite $\sqrt[4]{2^{2}}$ as $\sqrt{\sqrt{2^{2}}}$ .

$x = \pm 2 \sqrt{\sqrt{2^{2}}}$

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

$x = \pm 2 \sqrt{2}$

Step 3

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = 2 \sqrt{2}$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 2 \sqrt{2}$

The complete solution is the result of both the positive and negative portions of the solution.

$x = 2 \sqrt{2}, - 2 \sqrt{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = 2 \sqrt{2}, - 2 \sqrt{2}$

Decimal Form:

$x = 2.82842712 \dots, - 2.82842712 \dots$