The exponent is 12 (512). 512 = 244,140,625
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Power = 5 = exponent. That is, exponent = 5.
105 is a power. 10 is the base and the exponent is 5.
In the number 25 the exponent is 5. Whereas, 2 is the base.
I am not entirely sure what you mean: If you raise something to a power, you automatically have an exponent.(-5) to the power (-1) is the reciprocal of (-5) to the power 1, so you have 1 / (-5), or -1/5.
As far as I know, there is no no word that describes the exponent 5, besides the phrase "raised to the fifth power".