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You are correct. The “2nd power of 5” is equivalent to “5^{2},” which, of course, means 5 × 5 ( = 25).

Special terminology is used to describe a quantity written in the form of a power of a number. The number that is to be used as a factor is called the base. The number telling how many times the base is to be used as a factor is called the exponent:

base → 5^{2 ← exponent}

Powers of numbers are very important in the study of number systems. We therefore need a convenient symbol to stand for the idea of powers. We shall use the letter b to stand for the base. We shall use the letter n to stand for the number of times the base is used as a factor. The letter n is the exponent of b. Thus the symbol for any power of any number is

b^{n}

By using this symbol, we can make general statements about powers without needing specific examples, just as we can make general statements about addition or multiplication.

If a quantity is written as a power, and the base of the quantity is 3 and the exponent is 2, what is the quantity?