Precalculus Examples

${(\frac{b}{3})}^{4} = 10$

Step 1

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

$\frac{b}{3} = \pm \sqrt[4]{10}$

Step 2

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

Tap for more steps...

Step 2.1

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

$\frac{b}{3} = \sqrt[4]{10}$

Step 2.2

Multiply both sides of the equation by $3$ .

$3 \frac{b}{3} = 3 \sqrt[4]{10}$

Step 2.3

Simplify the left side.

Tap for more steps...

Step 2.3.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.3.1.1

Cancel the common factor.

$3 \frac{b}{3} = 3 \sqrt[4]{10}$

Step 2.3.1.2

Rewrite the expression.

$b = 3 \sqrt[4]{10}$

Step 2.4

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

$\frac{b}{3} = - \sqrt[4]{10}$

Step 2.5

Multiply both sides of the equation by $3$ .

$3 \frac{b}{3} = 3 (- \sqrt[4]{10})$

Step 2.6

Simplify both sides of the equation.

Tap for more steps...

Step 2.6.1

Simplify the left side.

Tap for more steps...

Step 2.6.1.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.6.1.1.1

Cancel the common factor.

$3 \frac{b}{3} = 3 (- \sqrt[4]{10})$

Step 2.6.1.1.2

Rewrite the expression.

$b = 3 (- \sqrt[4]{10})$

Step 2.6.2

Simplify the right side.

Tap for more steps...

Step 2.6.2.1

Multiply $- 1$ by $3$ .

$b = - 3 \sqrt[4]{10}$

Step 2.7

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

$b = 3 \sqrt[4]{10}, - 3 \sqrt[4]{10}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$b = 3 \sqrt[4]{10}, - 3 \sqrt[4]{10}$

Decimal Form:

$b = 5.33483823 \dots, - 5.33483823 \dots$