Question

IF a#b=a^b-2ab=b^b(-a)^b+b^b then find4#(-3)
sign^=multiplication

Answer 1

I have a feeling that your definition of a#b
contains a typo. I have suspicions about that second equal sign. Since the + and the = are on the same key on your keyboard, I suspect it should be +

a#b=a^b-2ab + b^b(-a)^b+b^b
4#(-3) = 4^(-3) - 2(4)(-3) + (-3)^(-3) (-4)^(-3) + (-3)^-3
= 1/4^3 + 24 + 1/(-3)^3 (1/(-4)^3) + 1/(-3)^3
= 1/64 + 24 + (-1/27)(-1/64) - 1/27
= 1/64 + 24 + 1/1728 - 1/27
= 1151/48

check my arithmetic, I should have written it out on paper first.

Just noticed that you said your ^ means multiplication. Then what does ab mean??
For online math symbols the ^ is used for exponentiation.