why is b raised to the power of 0 =1 ?{b|b is not equal to zero}?

Answer 1

Any number to the zero power is 1.

Example:

b=5

b^0=?
b^1=5
b^2=25
b^3=125

Notice how each time I add one to the power, I multiply by 5? If I lower the power by 1, I divide by 5.

b^3=125
b^2=25
b^1=5
b^0=1
b^-1=1/5

Hope that makes sense!

Answer 2

Mostly, it's a definition.
If you think of b raised to the power x, it means you have "x" b's that you multiply together. If you have NO b's to multiply together, there isn't really an answer at all.
But, to make other things in mathematics work consistently, it's beter to define this as 1 than 0.
For example -- b to the x times b to the y = b to the (x+y), so if x is zero, you need b to the x to be equal to 1.