Solve for x x^4=16/625

$x^{4} = \frac{16}{625}$

Take the 4th root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt[4]{\frac{16}{625}}$

Simplify $\pm \sqrt[4]{\frac{16}{625}}$ .

Rewrite $\sqrt[4]{\frac{16}{625}}$ as $\frac{\sqrt[4]{16}}{\sqrt[4]{625}}$ .

$x = \pm \frac{\sqrt[4]{16}}{\sqrt[4]{625}}$

Simplify the numerator.

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

$x = \pm \frac{\sqrt[4]{2^{4}}}{\sqrt[4]{625}}$

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

$x = \pm \frac{2}{\sqrt[4]{625}}$

Simplify the denominator.

Rewrite $625$ as $5^{4}$ .

$x = \pm \frac{2}{\sqrt[4]{5^{4}}}$

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

$x = \pm \frac{2}{5}$

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.

$x = \frac{2}{5}$

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

$x = - \frac{2}{5}$

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

$x = \frac{2}{5}, - \frac{2}{5}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{2}{5}, - \frac{2}{5}$

Decimal Form:

$x = 0.4, - 0.4$