How do you simplify #2^ 0#?
For any non-zero number
#a^0 = 1#
Here's one way of thinking of it:
#2*n = overbrace(2+2+...+2)^(n color(white)(x)"times")#
#2^n = overbrace(2xx2xx...xx2)^(n color(white)(x)"times")#
anything powered zero is equal to one
Because we know that a number divided by itself is 1.
And as you may already know, when you divide exponents you just subtract them.
There is also a pattern:
Same base, decrease the exponent by 1 and get half the value