Answer:
[tex]\textsf{Option 3}: \quad -10 x^2y^2-16x^{-2}y^2+8x^{-1}y^3[/tex]
Step-by-step explanation:
Given expression:
[tex]-2x^{-3}y(5yx^5+8xy-4y^2x^2)[/tex]
Distribute:
[tex]\implies -2x^{-3}y(5yx^5) -2x^{-3}y(8xy)-2x^{-3}y(-4y^2x^2)[/tex]
Multiply the constants and collect like terms:
[tex]\implies -10 x^{-3}x^5yy-16x^{-3}xyy+8x^{-3}x^2yy^2[/tex]
Remember that a = a¹.
[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]
[tex]\implies -10 x^{(-3+5)}y^{(1+1)}-16x^{(-3+1)}y^{(1+1)}+8x^{(-3+2)}y^{(1+2)}[/tex]
[tex]\implies -10 x^2y^2-16x^{-2}y^2+8x^{-1}y^3[/tex]
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