Algebra Examples

$\frac{x^{- 6} \cdot x^{- 3}}{x^{- 8}}$

Step 1

Multiply $x^{- 6}$ by $x^{- 3}$ 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.

$\frac{x^{- 6 - 3}}{x^{- 8}}$

Step 1.2

Subtract $3$ from $- 6$ .

$\frac{x^{- 9}}{x^{- 8}}$

Step 2

Move $x^{- 9}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{x^{- 8} x^{9}}$

Step 3

Simplify the denominator.

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Step 3.1

Multiply $x^{- 8}$ by $x^{9}$ by adding the exponents.

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Step 3.1.1

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

$\frac{1}{x^{- 8 + 9}}$

Step 3.1.2

Add $- 8$ and $9$ .

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

Step 3.2

Simplify $x^{1}$ .

$\frac{1}{x}$