Evaluate (y^-1y^-5)/(x^8x^-2)

$\frac{y^{- 1} y^{- 5}}{x^{8} x^{- 2}}$

Step 1

Multiply $y^{- 1}$ by $y^{- 5}$ by adding the exponents.

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

$\frac{y^{- 1 - 5}}{x^{8} x^{- 2}}$

Subtract $5$ from $- 1$ .

$\frac{y^{- 6}}{x^{8} x^{- 2}}$

Step 2

Multiply $x^{8}$ by $x^{- 2}$ by adding the exponents.

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

$\frac{y^{- 6}}{x^{8 - 2}}$

Subtract $2$ from $8$ .

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

Step 3

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

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