Finite Math Examples

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

Step 1

Subtract $3$ from both sides of the equation.

$4 \sqrt[4]{b} - 3 = 0$

Step 2

Add $3$ to both sides of the equation.

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

Step 3

To remove the radical on the left side of the equation, raise both sides of the equation to the power of $4$ .

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

Step 4

Simplify each side of the equation.

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Step 4.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{b}$ as $b^{\frac{1}{4}}$ .

${(4 b^{\frac{1}{4}})}^{4} = 3^{4}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Simplify ${(4 b^{\frac{1}{4}})}^{4}$ .

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Step 4.2.1.1

Apply the product rule to $4 b^{\frac{1}{4}}$ .

$4^{4} {(b^{\frac{1}{4}})}^{4} = 3^{4}$

Step 4.2.1.2

Raise $4$ to the power of $4$ .

$256 {(b^{\frac{1}{4}})}^{4} = 3^{4}$

Step 4.2.1.3

Multiply the exponents in ${(b^{\frac{1}{4}})}^{4}$ .

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Step 4.2.1.3.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$256 b^{\frac{1}{4} \cdot 4} = 3^{4}$

Step 4.2.1.3.2

Cancel the common factor of $4$ .

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Step 4.2.1.3.2.1

Cancel the common factor.

$256 b^{\frac{1}{4} \cdot 4} = 3^{4}$

Step 4.2.1.3.2.2

Rewrite the expression.

$256 b^{1} = 3^{4}$

Step 4.2.1.4

Simplify.

$256 b = 3^{4}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Raise $3$ to the power of $4$ .

$256 b = 81$

Step 5

Divide each term in $256 b = 81$ by $256$ and simplify.

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Step 5.1

Divide each term in $256 b = 81$ by $256$ .

$\frac{256 b}{256} = \frac{81}{256}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $256$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{256 b}{256} = \frac{81}{256}$

Step 5.2.1.2

Divide $b$ by $1$ .

$b = \frac{81}{256}$