what is the value of 3^0+3^-2

By definition anything raised to the zero power = 1

3^-2 is the same as 1/3^2

Not to confuse the issue, but it is easy to show that anything to the zero power = 1.

Take a fraction of
3/3 we know that is 1

use exponents 3^1 / 3^1 = following our rules for exponents we would have 3^(1-1) or 3^0 = 1