Find the Roots (Zeros) 16x^4-81=0

$16 x^{4} - 81 = 0$

Step 1

Add $81$ to both sides of the equation.

$16 x^{4} = 81$

Step 2

Divide each term in $16 x^{4} = 81$ by $16$ and simplify.

Divide each term in $16 x^{4} = 81$ by $16$ .

$\frac{16 x^{4}}{16} = \frac{81}{16}$

Simplify the left side.

Cancel the common factor of $16$ .

Cancel the common factor.

$\frac{16 x^{4}}{16} = \frac{81}{16}$

Divide $x^{4}$ by $1$ .

$x^{4} = \frac{81}{16}$

Step 3

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

$x = \pm \sqrt[4]{\frac{81}{16}}$

Step 4

Simplify $\pm \sqrt[4]{\frac{81}{16}}$ .

Rewrite $\sqrt[4]{\frac{81}{16}}$ as $\frac{\sqrt[4]{81}}{\sqrt[4]{16}}$ .

$x = \pm \frac{\sqrt[4]{81}}{\sqrt[4]{16}}$

Simplify the numerator.

Rewrite $81$ as $3^{4}$ .

$x = \pm \frac{\sqrt[4]{3^{4}}}{\sqrt[4]{16}}$

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

$x = \pm \frac{3}{\sqrt[4]{16}}$

Simplify the denominator.

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

$x = \pm \frac{3}{\sqrt[4]{2^{4}}}$

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

$x = \pm \frac{3}{2}$

Step 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.

$x = \frac{3}{2}$

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

$x = - \frac{3}{2}$

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

$x = \frac{3}{2}, - \frac{3}{2}$

Step 6