Precalculus Examples

$f (x) = \sqrt[5]{x - 4} + 2$

Step 1

Set $\sqrt[5]{x - 4} + 2$ equal to $0$ .

$\sqrt[5]{x - 4} + 2 = 0$

Step 2

Solve for $x$ .

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Step 2.1

Subtract $2$ from both sides of the equation.

$\sqrt[5]{x - 4} = - 2$

Step 2.2

To remove the radical on the left side of the equation, raise both sides of the equation to the power of $5$ .

${\sqrt[5]{x - 4}}^{5} = {(- 2)}^{5}$

Step 2.3

Simplify each side of the equation.

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Step 2.3.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[5]{x - 4}$ as ${(x - 4)}^{\frac{1}{5}}$ .

${({(x - 4)}^{\frac{1}{5}})}^{5} = {(- 2)}^{5}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Simplify ${({(x - 4)}^{\frac{1}{5}})}^{5}$ .

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Step 2.3.2.1.1

Multiply the exponents in ${({(x - 4)}^{\frac{1}{5}})}^{5}$ .

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Step 2.3.2.1.1.1

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

${(x - 4)}^{\frac{1}{5} \cdot 5} = {(- 2)}^{5}$

Step 2.3.2.1.1.2

Cancel the common factor of $5$ .

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Step 2.3.2.1.1.2.1

Cancel the common factor.

${(x - 4)}^{\frac{1}{5} \cdot 5} = {(- 2)}^{5}$

Step 2.3.2.1.1.2.2

Rewrite the expression.

${(x - 4)}^{1} = {(- 2)}^{5}$

Step 2.3.2.1.2

Simplify.

$x - 4 = {(- 2)}^{5}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Raise $- 2$ to the power of $5$ .

$x - 4 = - 32$

Step 2.4

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

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Step 2.4.1

Add $4$ to both sides of the equation.

$x = - 32 + 4$

Step 2.4.2

Add $- 32$ and $4$ .

$x = - 28$

Step 3