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You are correct. The “2nd power of 5” is equivalent to “52,” 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 → 52 ← 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
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?