Simplify (x^-8)/(x^6*x^-7)

$\frac{x^{- 8}}{x^{6} \cdot x^{- 7}}$

Step 1

Multiply $x^{6}$ by $x^{- 7}$ by adding the exponents.

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

$\frac{x^{- 8}}{x^{6 - 7}}$

Subtract $7$ from $6$ .

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

Step 2

Move $x^{- 8}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 3

Multiply $x^{- 1}$ by $x^{8}$ by adding the exponents.

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

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

Add $- 1$ and $8$ .

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