Finite Math Examples

$\sqrt[4]{4 x - 1} = 3$

Step 1

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

${\sqrt[4]{4 x - 1}}^{4} = 3^{4}$

Step 2

Simplify each side of the equation.

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Step 2.1

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

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

Step 2.2

Simplify the left side.

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Step 2.2.1

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

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Step 2.2.1.1

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

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Step 2.2.1.1.1

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

${(4 x - 1)}^{\frac{1}{4} \cdot 4} = 3^{4}$

Step 2.2.1.1.2

Cancel the common factor of $4$ .

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Step 2.2.1.1.2.1

Cancel the common factor.

${(4 x - 1)}^{\frac{1}{4} \cdot 4} = 3^{4}$

Step 2.2.1.1.2.2

Rewrite the expression.

${(4 x - 1)}^{1} = 3^{4}$

Step 2.2.1.2

Simplify.

$4 x - 1 = 3^{4}$

Step 2.3

Simplify the right side.

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Step 2.3.1

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

$4 x - 1 = 81$

Step 3

Solve for $x$ .

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Step 3.1

Move all terms not containing $x$ to the right side of the equation.

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Step 3.1.1

Add $1$ to both sides of the equation.

$4 x = 81 + 1$

Step 3.1.2

Add $81$ and $1$ .

$4 x = 82$

Step 3.2

Divide each term in $4 x = 82$ by $4$ and simplify.

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Step 3.2.1

Divide each term in $4 x = 82$ by $4$ .

$\frac{4 x}{4} = \frac{82}{4}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $4$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{82}{4}$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{82}{4}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Cancel the common factor of $82$ and $4$ .

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Step 3.2.3.1.1

Factor $2$ out of $82$ .

$x = \frac{2 (41)}{4}$

Step 3.2.3.1.2

Cancel the common factors.

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Step 3.2.3.1.2.1

Factor $2$ out of $4$ .

$x = \frac{2 \cdot 41}{2 \cdot 2}$

Step 3.2.3.1.2.2

Cancel the common factor.

$x = \frac{2 \cdot 41}{2 \cdot 2}$

Step 3.2.3.1.2.3

Rewrite the expression.

$x = \frac{41}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{41}{2}$

Decimal Form:

$x = 20.5$

Mixed Number Form:

$x = 20 \frac{1}{2}$