Algebra Examples

${(\sqrt[4]{x - 5})}^{8}$

Step 1

Simplify by cancelling exponent with radical.

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Step 1.1

Rewrite ${\sqrt[4]{x - 5}}^{8}$ as ${(x - 5)}^{2}$ .

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Step 1.1.1

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

${({(x - 5)}^{\frac{1}{4}})}^{8}$

Step 1.1.2

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

${(x - 5)}^{\frac{1}{4} \cdot 8}$

Step 1.1.3

Combine $\frac{1}{4}$ and $8$ .

${(x - 5)}^{\frac{8}{4}}$

Step 1.1.4

Cancel the common factor of $8$ and $4$ .

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Step 1.1.4.1

Factor $4$ out of $8$ .

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

Step 1.1.4.2

Cancel the common factors.

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Step 1.1.4.2.1

Factor $4$ out of $4$ .

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

Step 1.1.4.2.2

Cancel the common factor.

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

Step 1.1.4.2.3

Rewrite the expression.

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

Step 1.1.4.2.4

Divide $2$ by $1$ .

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

Step 1.2

Rewrite ${(x - 5)}^{2}$ as $(x - 5) (x - 5)$ .

$(x - 5) (x - 5)$

Step 2

Expand $(x - 5) (x - 5)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$x (x - 5) - 5 (x - 5)$

Step 2.2

Apply the distributive property.

$x \cdot x + x \cdot - 5 - 5 (x - 5)$

Step 2.3

Apply the distributive property.

$x \cdot x + x \cdot - 5 - 5 x - 5 \cdot - 5$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 5 - 5 x - 5 \cdot - 5$

Step 3.1.2

Move $- 5$ to the left of $x$ .

$x^{2} - 5 \cdot x - 5 x - 5 \cdot - 5$

Step 3.1.3

Multiply $- 5$ by $- 5$ .

$x^{2} - 5 x - 5 x + 25$

Step 3.2

Subtract $5 x$ from $- 5 x$ .

$x^{2} - 10 x + 25$