Question

if a^0=b^0 then a=b ( true/false)

Answer 1

a^0 = 1
b^0 = 1

Given,
a^0 = b^0
1 = 1
So, the statement is true.

Answer 2

a^0 = b^0 is true off course. but a=b is false if given only that a^0= b^0 as any number with the power of 0 becomes 1.
For instance,
3^0=4^0(as, forms 1=1)
but 3 is not equal to 4