Algebra Examples

$\sqrt[4]{\frac{1}{3} x - 8} = 2$

Step 1

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

${\sqrt[4]{\frac{1}{3} x - 8}}^{4} = 2^{4}$

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 $\sqrt[4]{\frac{1}{3} x - 8}$ as ${(\frac{1}{3} x - 8)}^{\frac{1}{4}}$ .

${({(\frac{1}{3} x - 8)}^{\frac{1}{4}})}^{4} = 2^{4}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify ${({(\frac{1}{3} x - 8)}^{\frac{1}{4}})}^{4}$ .

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Step 2.2.1.1

Multiply the exponents in ${({(\frac{1}{3} x - 8)}^{\frac{1}{4}})}^{4}$ .

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Step 2.2.1.1.1

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

${(\frac{1}{3} x - 8)}^{\frac{1}{4} \cdot 4} = 2^{4}$

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.

${(\frac{1}{3} x - 8)}^{\frac{1}{4} \cdot 4} = 2^{4}$

Step 2.2.1.1.2.2

Rewrite the expression.

${(\frac{1}{3} x - 8)}^{1} = 2^{4}$

Step 2.2.1.2

Combine $\frac{1}{3}$ and $x$ .

${(\frac{x}{3} - 8)}^{1} = 2^{4}$

Step 2.2.1.3

Simplify.

$\frac{x}{3} - 8 = 2^{4}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Raise $2$ to the power of $4$ .

$\frac{x}{3} - 8 = 16$

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 $8$ to both sides of the equation.

$\frac{x}{3} = 16 + 8$

Step 3.1.2

Add $16$ and $8$ .

$\frac{x}{3} = 24$

Step 3.2

Multiply both sides of the equation by $3$ .

$3 \frac{x}{3} = 3 \cdot 24$

Step 3.3

Simplify both sides of the equation.

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Step 3.3.1

Simplify the left side.

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Step 3.3.1.1

Cancel the common factor of $3$ .

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Step 3.3.1.1.1

Cancel the common factor.

$3 \frac{x}{3} = 3 \cdot 24$

Step 3.3.1.1.2

Rewrite the expression.

$x = 3 \cdot 24$

Step 3.3.2

Simplify the right side.

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Step 3.3.2.1

Multiply $3$ by $24$ .

$x = 72$