Algebra Examples

$\frac{x^{- 7}}{x^{6} \cdot x^{- 5}}$

Step 1

Multiply $x^{6}$ by $x^{- 5}$ by adding the exponents.

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Step 1.1

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

$\frac{x^{- 7}}{x^{6 - 5}}$

Step 1.2

Subtract $5$ from $6$ .

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

Step 2

Simplify $x^{1}$ .

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

Step 3

Move $x^{- 7}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 4

Multiply $x$ by $x^{7}$ by adding the exponents.

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Step 4.1

Multiply $x$ by $x^{7}$ .

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Step 4.1.1

Raise $x$ to the power of $1$ .

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

Step 4.1.2

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

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

Step 4.2

Add $1$ and $7$ .

$\frac{1}{x^{8}}$