Algebra Examples

${(x)}^{- 1} {(x)}^{\frac{- 7}{8}} {(x)}^{\frac{1}{8}}$

Step 1

Move the negative in front of the fraction.

${(x)}^{- 1} x^{- \frac{7}{8}} {(x)}^{\frac{1}{8}}$

Step 2

Multiply ${(x)}^{- 1}$ by $x^{- \frac{7}{8}}$ by adding the exponents.

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Step 2.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{- 1 - \frac{7}{8}} {(x)}^{\frac{1}{8}}$

Step 2.2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$x^{- 1 \cdot \frac{8}{8} - \frac{7}{8}} {(x)}^{\frac{1}{8}}$

Step 2.3

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

$x^{\frac{- 1 \cdot 8}{8} - \frac{7}{8}} {(x)}^{\frac{1}{8}}$

Step 2.4

Combine the numerators over the common denominator.

$x^{\frac{- 1 \cdot 8 - 7}{8}} {(x)}^{\frac{1}{8}}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $- 1$ by $8$ .

$x^{\frac{- 8 - 7}{8}} {(x)}^{\frac{1}{8}}$

Step 2.5.2

Subtract $7$ from $- 8$ .

$x^{\frac{- 15}{8}} {(x)}^{\frac{1}{8}}$

Step 2.6

Move the negative in front of the fraction.

$x^{- \frac{15}{8}} {(x)}^{\frac{1}{8}}$

Step 3

Multiply $x^{- \frac{15}{8}}$ by ${(x)}^{\frac{1}{8}}$ by adding the exponents.

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Step 3.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{- \frac{15}{8} + \frac{1}{8}}$

Step 3.2

Combine the numerators over the common denominator.

$x^{\frac{- 15 + 1}{8}}$

Step 3.3

Add $- 15$ and $1$ .

$x^{\frac{- 14}{8}}$

Step 3.4

Cancel the common factor of $- 14$ and $8$ .

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Step 3.4.1

Factor $2$ out of $- 14$ .

$x^{\frac{2 (- 7)}{8}}$

Step 3.4.2

Cancel the common factors.

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Step 3.4.2.1

Factor $2$ out of $8$ .

$x^{\frac{2 \cdot - 7}{2 \cdot 4}}$

Step 3.4.2.2

Cancel the common factor.

$x^{\frac{2 \cdot - 7}{2 \cdot 4}}$

Step 3.4.2.3

Rewrite the expression.

$x^{\frac{- 7}{4}}$

Step 3.5

Move the negative in front of the fraction.

$x^{- \frac{7}{4}}$

Step 4

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{x^{\frac{7}{4}}}$

Step 5

Apply the rule $x^{\frac{m}{n}} = \sqrt[n]{x^{m}}$ to rewrite the exponentiation as a radical.

$\frac{1}{\sqrt[4]{x^{7}}}$