Evaluate (x^-6)/(x^-2y^-2y^-5)

$\frac{x^{- 6}}{x^{- 2} y^{- 2} y^{- 5}}$

Step 1

Multiply $y^{- 2}$ by $y^{- 5}$ by adding the exponents.

Move $y^{- 5}$ .

$\frac{x^{- 6}}{x^{- 2} (y^{- 5} y^{- 2})}$

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

$\frac{x^{- 6}}{x^{- 2} y^{- 5 - 2}}$

Subtract $2$ from $- 5$ .

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

Step 2

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

$\frac{1}{x^{- 2} y^{- 7} x^{6}}$

Step 3

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

Move $x^{6}$ .

$\frac{1}{x^{6} x^{- 2} y^{- 7}}$

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

$\frac{1}{x^{6 - 2} y^{- 7}}$

Subtract $2$ from $6$ .

$\frac{1}{x^{4} y^{- 7}}$

Step 4

Move $y^{- 7}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{y^{7}}{x^{4}}$