Evaluate x^2y^-4*x^3y^2

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

Step 1

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

Move $x^{3}$ .

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

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

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

Add $3$ and $2$ .

$x^{5} y^{- 4} \cdot y^{2}$

Step 2

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

Move $y^{2}$ .

$x^{5} (y^{2} y^{- 4})$

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

$x^{5} y^{2 - 4}$

Subtract $4$ from $2$ .

$x^{5} y^{- 2}$

Step 3

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 4

Combine $x^{5}$ and $\frac{1}{y^{2}}$ .

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