Simplify x^3y^-1xyx^-2y^2

$x^{3} y^{- 1} \cdot x y \cdot x^{- 2} y^{2}$

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

Move $x$ .

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

Multiply $x$ by $x^{3}$ .

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

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

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

$x^{1 + 3} y^{- 1} \cdot y \cdot (x^{- 2} y^{2})$

Add $1$ and $3$ .

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

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

Move $x^{- 2}$ .

$x^{- 2} x^{4} y^{- 1} \cdot y \cdot y^{2}$

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

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

Add $- 2$ and $4$ .

$x^{2} y^{- 1} \cdot y \cdot y^{2}$

Multiply $y^{- 1}$ by $y$ by adding the exponents.

Move $y$ .

$x^{2} (y \cdot y^{- 1}) \cdot y^{2}$

Multiply $y$ by $y^{- 1}$ .

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

$x^{2} (y^{1} y^{- 1}) \cdot y^{2}$

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

$x^{2} y^{1 - 1} \cdot y^{2}$

Subtract $1$ from $1$ .

$x^{2} y^{0} \cdot y^{2}$

Simplify $x^{2} y^{0} \cdot y^{2}$ .

$x^{2} y^{2}$

Simplify x^3y^-1*xy*x^-2y^2