Simplify (2x^-3y^2)/(x^-3y^-3)

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

Step 1

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

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

Step 2

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

Move $y^{3}$ .

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

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

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

Add $3$ and $2$ .

$\frac{2 x^{- 3} y^{5}}{x^{- 3}}$

Step 3

Cancel the common factor of $x^{- 3}$ .

Cancel the common factor.

$\frac{2 x^{- 3} y^{5}}{x^{- 3}}$

Divide $2 y^{5}$ by $1$ .

$2 y^{5}$