Simplify (x^2y^-3)/(3y^2)*(y^2)/(x^-4)

$\frac{x^{2} y^{- 3}}{3 y^{2}} \cdot \frac{y^{2}}{x^{- 4}}$

Step 1

Combine.

$\frac{x^{2} y^{- 3} y^{2}}{3 y^{2} x^{- 4}}$

Step 2

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

Move $y^{2}$ .

$\frac{x^{2} (y^{2} y^{- 3})}{3 y^{2} x^{- 4}}$

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

$\frac{x^{2} y^{2 - 3}}{3 y^{2} x^{- 4}}$

Subtract $3$ from $2$ .

$\frac{x^{2} y^{- 1}}{3 y^{2} x^{- 4}}$

Step 3

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

$\frac{x^{2}}{3 y^{2} x^{- 4} y}$

Step 4

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

Move $y$ .

$\frac{x^{2}}{3 (y \cdot y^{2}) x^{- 4}}$

Multiply $y$ by $y^{2}$ .

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

$\frac{x^{2}}{3 (y^{1} y^{2}) x^{- 4}}$

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

$\frac{x^{2}}{3 y^{1 + 2} x^{- 4}}$

Add $1$ and $2$ .

$\frac{x^{2}}{3 y^{3} x^{- 4}}$

Step 5

Move $x^{- 4}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{x^{2} x^{4}}{3 y^{3}}$

Step 6

Multiply $x^{2}$ by $x^{4}$ by adding the exponents.

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

$\frac{x^{2 + 4}}{3 y^{3}}$

Add $2$ and $4$ .

$\frac{x^{6}}{3 y^{3}}$