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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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Q: What is base and exponent of 625?

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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.

The base and exponent form a pair. You can chose any positive base and that will determine the exponent.243 = 49^1.5 that is base = 49, exponent = 1.5)or 243 = 10^2.5353 (approx) or 243 = 7^3.

base

Related questions

54

625/5

5^4

yes. 5 x 5 x 5 x 5 = 625

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 of an exponent is the main number. For example in 56 the number 5 is the base and 6 is the exponent.

If you have ab then a is the base and b the exponent

4 is the base, 2 is the exponent.

10x 10 is Base & x is exponent

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)

For 104 the base is 10 and the exponent is 4.

The base is 7 and the exponent is 3.

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