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
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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.
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.
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.