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You can choose the base to be any number (other than 0, -1 and 1) and calculate the appropriate exponent, or you can choose any exponent and calculate the appropriate base.
For example, base 10: 121 = 10^2.08278537 (approx)
Or exponent = 10: 121 = 1.615394266^10 (approx).
I expect, though, that the answer that is required is 121 = 11^2.
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What is the base and exponent of 121?
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)
What is the exponent and base for 262144?
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 is 7 and the exponent is 3.
What is base and exponent of 625?
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.
What are the Exponent rules?
base
