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

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

Step 1

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

Multiply $x$ by $x^{- 2}$ .

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

$\frac{x^{- 6}}{x^{1} \cdot x^{- 2}}$

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

$\frac{x^{- 6}}{x^{1 - 2}}$

Subtract $2$ from $1$ .

$\frac{x^{- 6}}{x^{- 1}}$

Step 2

Move $x^{- 6}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{x^{- 1} x^{6}}$

Step 3

Multiply $x^{- 1}$ by $x^{6}$ by adding the exponents.

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

$\frac{1}{x^{- 1 + 6}}$

Add $- 1$ and $6$ .

$\frac{1}{x^{5}}$