Evaluate (x^-6y^-1y)/(x^2)

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

Step 1

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

Move $y$ .

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

Multiply $y$ by $y^{- 1}$ .

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

$\frac{x^{- 6} (y^{1} y^{- 1})}{x^{2}}$

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

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

Subtract $1$ from $1$ .

$\frac{x^{- 6} y^{0}}{x^{2}}$

Step 2

Simplify $x^{- 6} y^{0}$ .

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

Step 3

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

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

Step 4

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

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

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

Add $2$ and $6$ .

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