Simplify 10x^3y*3x^-3y

$10 x^{3} y \cdot 3 x^{- 3} y$

Step 1

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

Move $x^{- 3}$ .

$10 (x^{- 3} x^{3}) y \cdot (3 y)$

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

$10 x^{- 3 + 3} y \cdot (3 y)$

Add $- 3$ and $3$ .

$10 x^{0} y \cdot (3 y)$

Step 2

Simplify $10 x^{0} y \cdot (3 y)$ .

$10 y \cdot (3 y)$

Step 3

Rewrite using the commutative property of multiplication.

$10 \cdot 3 y \cdot y$

Step 4

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

$10 \cdot 3 (y \cdot y)$

Multiply $y$ by $y$ .

$10 \cdot 3 y^{2}$

Step 5

Multiply $10$ by $3$ .

$30 y^{2}$