The first exponent is 25m2.
The second exponent is m2.
Because the two initial bases are both 5, we may add the exponents getting
525m^2 + 5m^2 = 530m^2
Alternately, and more simply we can substitute in m =1 to demonstrate they are not the same.
525(1) * 51 = 526 which is not the same as 2510 = 255(1) + 5
See ** below.
Watch for a subtle and very obsure error. When dealing with exponent of exponents, it's important to identify where the higher level exponent is applying.
5 m^2 I'm interpreting as 5 (m^2) where the square only applies to m. This is very different from ( 5 m ) ^2 = (5 m) * (5 m) where the square applies to the entire 5m
Try with m = 2 to prove they are different.
** Special note: Examples, like m=1, can prove a statement false. However, examples can never prove a statement with variables or a theorem true.