Precalculus Examples

$\frac{\frac{3}{16}}{3} = \frac{3 b^{4}}{3}$

Step 1

Rewrite the equation as $\frac{3 b^{4}}{3} = \frac{\frac{3}{16}}{3}$ .

$\frac{3 b^{4}}{3} = \frac{\frac{3}{16}}{3}$

Step 2

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$3 b^{4} = \frac{3}{16}$

Step 3

Divide each term in $3 b^{4} = \frac{3}{16}$ by $3$ and simplify.

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Step 3.1

Divide each term in $3 b^{4} = \frac{3}{16}$ by $3$ .

$\frac{3 b^{4}}{3} = \frac{\frac{3}{16}}{3}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $3$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{3 b^{4}}{3} = \frac{\frac{3}{16}}{3}$

Step 3.2.1.2

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

$b^{4} = \frac{\frac{3}{16}}{3}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Multiply the numerator by the reciprocal of the denominator.

$b^{4} = \frac{3}{16} \cdot \frac{1}{3}$

Step 3.3.2

Cancel the common factor of $3$ .

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Step 3.3.2.1

Cancel the common factor.

$b^{4} = \frac{3}{16} \cdot \frac{1}{3}$

Step 3.3.2.2

Rewrite the expression.

$b^{4} = \frac{1}{16}$

Step 4

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

$b = \pm \sqrt[4]{\frac{1}{16}}$

Step 5

Simplify $\pm \sqrt[4]{\frac{1}{16}}$ .

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Step 5.1

Rewrite $\sqrt[4]{\frac{1}{16}}$ as $\frac{\sqrt[4]{1}}{\sqrt[4]{16}}$ .

$b = \pm \frac{\sqrt[4]{1}}{\sqrt[4]{16}}$

Step 5.2

Any root of $1$ is $1$ .

$b = \pm \frac{1}{\sqrt[4]{16}}$

Step 5.3

Simplify the denominator.

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Step 5.3.1

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

$b = \pm \frac{1}{\sqrt[4]{2^{4}}}$

Step 5.3.2

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

$b = \pm \frac{1}{2}$

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.

$b = \frac{1}{2}$

Step 6.2

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

$b = - \frac{1}{2}$

Step 6.3

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

$b = \frac{1}{2}, - \frac{1}{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$b = \frac{1}{2}, - \frac{1}{2}$

Decimal Form:

$b = 0.5, - 0.5$