The base is 7 and the exponent is 3.
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The base is the large number, and is the number being multiplied; the exponent is the smaller number on the upper right, which says how many times the base is multiplied. 23 says that 2 is multiplied 3 times, so: 2 X 2 X 2. In this case, the base is 2, 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 and exponent are the two parts of a power. The base is the lower left, normal-sized, number. The exponent is the upper-right, small (i.e., superscript) number. For example, in: 34 3 is the base, 4 is the exponent. In the simplest case, a power specifies a repeated multiplication. The base tells you what number to multiply by itself, the exponent tells you how many times to multiply it. Thus, 34 = 3 x 3 x 3 x 3 (that is, multiply 3 by itself, using the number 4 times as a factor)
What a number is raised to. Three (the base) to the third power = 33 = 3*3*3 The power or the exponent tells us how many times the base takes place in a repeated multiplication.
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.