What is base and exponent of 625?

Answer 1

You can define any base you like and calculate an appropriate exponent or, you can pick an exponent and calculate the base.

So you can have

base 25, with exponent 2

or base 5 and exonent 4

or base e (the base for natural logarithms) and exponent 6.437752 (to 6 dp)

or base 10 and exponent 2.795880 (to 6 dp)

or base 2 and exponent 9.287712

etc

or base 8.54988 (to 3 dp) and exponent 3

or base 3.623898 (to 3 dp) and exponent 5

etc

There is no need for the base to be an integer or even rational. Probably the most important bases in advanced mathematics is e, which is a transcendental number. Similarly, there is no need for the exponent to be an integer.

Answer 2

24