Simplify (x^-7)/(x^-6*x^-2)

$\frac{x^{- 7}}{x^{- 6} \cdot x^{- 2}}$

Step 1

Multiply $x^{- 6}$ by $x^{- 2}$ by adding the exponents.

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

$\frac{x^{- 7}}{x^{- 6 - 2}}$

Subtract $2$ from $- 6$ .

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

Step 2

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

$x^{- 7} x^{8}$

Step 3

Multiply $x^{- 7}$ by $x^{8}$ by adding the exponents.

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

$x^{- 7 + 8}$

Add $- 7$ and $8$ .

$x^{1}$

Step 4

Simplify $x^{1}$ .

$x$