Evaluate 2x^3y^-3*2x^-1y^3

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

Step 1

Multiply $x^{3}$ by $x^{- 1}$ by adding the exponents.

Move $x^{- 1}$ .

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

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

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

Add $- 1$ and $3$ .

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

Step 2

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

Move $y^{3}$ .

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

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

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

Subtract $3$ from $3$ .

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

Step 3

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

$2 x^{2} \cdot 2$

Step 4

Multiply $2$ by $2$ .

$4 x^{2}$