Trigonometry Examples

$z^{4} = 81$

Step 1

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

$z = \pm \sqrt[4]{81}$

Step 2

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

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Step 2.1

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

$z = \pm \sqrt[4]{3^{4}}$

Step 2.2

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

$z = \pm 3$

Step 3

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

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Step 3.1

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

$z = 3$

Step 3.2

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

$z = - 3$

Step 3.3

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

$z = 3, - 3$