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.
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The two are related. The answer could be base 2, exponent 18 or base 8, exponent 6 or base 10, exponent 5.4185 or base 262144, exponent 1 or base 68,719,476,736 and exponent 0.5
The base could be 11 and the exponent 2, giving 112 But, it could equally be base = 14641, and exponent = 0.5, or base = 10, and exponent = 2.082785 (approx)
The base is 7 and the exponent is 3.
base
"The base of the exponent" doesn't make sense; base and exponent are two different parts of an exponential function. To be an exponential function, the variable must be in the exponent. Assuming the base is positive:* If the base is greater than 1, the function increases. * If the base is 1, you have a constant function. * If the base is less than 1, the function decreases.