Question

Multiply -2x^-3 y(5yx^5+8xy-4y^2x^2).

Answer 1

Answer:

$\textsf{Option 3}: \quad -10 x^2y^2-16x^{-2}y^2+8x^{-1}y^3$

Step-by-step explanation:

Given expression:

$-2x^{-3}y(5yx^5+8xy-4y^2x^2)$

Distribute:

$\implies -2x^{-3}y(5yx^5) -2x^{-3}y(8xy)-2x^{-3}y(-4y^2x^2)$

Multiply the constants and collect like terms:

$\implies -10 x^{-3}x^5yy-16x^{-3}xyy+8x^{-3}x^2yy^2$

Remember that a = a¹.

$\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:$

$\implies -10 x^{(-3+5)}y^{(1+1)}-16x^{(-3+1)}y^{(1+1)}+8x^{(-3+2)}y^{(1+2)}$

$\implies -10 x^2y^2-16x^{-2}y^2+8x^{-1}y^3$

Learn more about exponent rules here:

https://brainly.com/question/27745064

https://brainly.com/question/27959936