Evaluate (x^-3y^-3)/(x^-8y^2)

$\frac{x^{- 3} y^{- 3}}{x^{- 8} y^{2}}$

Step 1

Move $y^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{x^{- 3}}{x^{- 8} y^{2} y^{3}}$

Step 2

Multiply $y^{2}$ by $y^{3}$ by adding the exponents.

Move $y^{3}$ .

$\frac{x^{- 3}}{x^{- 8} (y^{3} y^{2})}$

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

$\frac{x^{- 3}}{x^{- 8} y^{3 + 2}}$

Add $3$ and $2$ .

$\frac{x^{- 3}}{x^{- 8} y^{5}}$

Step 3

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

$\frac{x^{- 3} x^{8}}{y^{5}}$

Step 4

Multiply $x^{- 3}$ by $x^{8}$ by adding the exponents.

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

$\frac{x^{- 3 + 8}}{y^{5}}$

Add $- 3$ and $8$ .

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