Basic Math Examples

$4 = \frac{K^{8}}{9}$

Step 1

Rewrite the equation as $\frac{K^{8}}{9} = 4$ .

$\frac{K^{8}}{9} = 4$

Step 2

Multiply both sides of the equation by $9$ .

$9 \frac{K^{8}}{9} = 9 \cdot 4$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $9$ .

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Step 3.1.1.1

Cancel the common factor.

$9 \frac{K^{8}}{9} = 9 \cdot 4$

Step 3.1.1.2

Rewrite the expression.

$K^{8} = 9 \cdot 4$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $9$ by $4$ .

$K^{8} = 36$

Step 4

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

$K = \pm \sqrt[8]{36}$

Step 5

Simplify $\pm \sqrt[8]{36}$ .

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Step 5.1

Rewrite $36$ as $6^{2}$ .

$K = \pm \sqrt[8]{6^{2}}$

Step 5.2

Rewrite $\sqrt[8]{6^{2}}$ as $\sqrt[4]{\sqrt{6^{2}}}$ .

$K = \pm \sqrt[4]{\sqrt{6^{2}}}$

Step 5.3

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

$K = \pm \sqrt[4]{6}$

Step 6

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

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Step 6.1

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

$K = \sqrt[4]{6}$

Step 6.2

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

$K = - \sqrt[4]{6}$

Step 6.3

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

$K = \sqrt[4]{6}, - \sqrt[4]{6}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$K = \sqrt[4]{6}, - \sqrt[4]{6}$

Decimal Form:

$K = 1.56508458 \dots, - 1.56508458 \dots$