Given that the absolute values of (x+y-1) and x+2 are mutually opposite, and a, b are mutually reciprocal, try to find the value of y power +ab of x?

Given that the absolute values of (x+y-1) and x+2 are mutually opposite, and a, b are mutually reciprocal, try to find the value of y power +ab of x?

A number whose absolute values are mutually opposite is 0
So X+Y-1=0, and X+2=0
I.e. X=-2, Y=3.
A, b are reciprocal, i.e. a=1/b. or ab=1
So y power of x +ab=-8+1=-7

If the absolute value of a+3 is opposite to the second power of (b-2), what is the value of the b-th power of ab-a? If the absolute value of a+3 is opposite to the second power of (b-2), what is the value of b-th power of ab-a?

The absolute value of a+3 is opposite to the second power of (b-2)
Absolute square ≥0
So only the opposite of 0 is 0
I.e. the absolute value of a+3=0; the second power of (b-2)=0
Solve a=-3, b=2
Ab-a^b
=-6-9
=-15