Simplify (2x^2y^3)(-5x^-2y^7)

$(2 x^{2} y^{3}) (- 5 x^{- 2} y^{7})$

Step 1

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

Move $x^{- 2}$ .

$2 (x^{- 2} x^{2}) y^{3} (- 5 y^{7})$

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

$2 x^{- 2 + 2} y^{3} (- 5 y^{7})$

Add $- 2$ and $2$ .

$2 x^{0} y^{3} (- 5 y^{7})$

Step 2

Simplify $2 x^{0} y^{3} (- 5 y^{7})$ .

$2 y^{3} (- 5 y^{7})$

Step 3

Rewrite using the commutative property of multiplication.

$2 \cdot - 5 y^{3} y^{7}$

Step 4

Multiply $y^{3}$ by $y^{7}$ by adding the exponents.

Move $y^{7}$ .

$2 \cdot - 5 (y^{7} y^{3})$

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

$2 \cdot - 5 y^{7 + 3}$

Add $7$ and $3$ .

$2 \cdot - 5 y^{10}$

Step 5

Multiply $2$ by $- 5$ .

$- 10 y^{10}$