Precalculus Examples

${(\sqrt[3]{x - 5})}^{3} + 1$

Step 1

Rewrite ${\sqrt[3]{x - 5}}^{3}$ as $x - 5$ .

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Step 1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{x - 5}$ as ${(x - 5)}^{\frac{1}{3}}$ .

${({(x - 5)}^{\frac{1}{3}})}^{3} + 1$

Step 1.2

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

${(x - 5)}^{\frac{1}{3} \cdot 3} + 1$

Step 1.3

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

${(x - 5)}^{\frac{3}{3}} + 1$

Step 1.4

Cancel the common factor of $3$ .

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Step 1.4.1

Cancel the common factor.

${(x - 5)}^{\frac{3}{3}} + 1$

Step 1.4.2

Rewrite the expression.

${(x - 5)}^{1} + 1$

Step 1.5

Simplify.

$x - 5 + 1$

Step 2

Add $- 5$ and $1$ .

$x - 4$