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“Two to the What?”: ‘Powers’ of Numbers
If you’re reading this, I guess you really don’t know what exponents are, or “powers of two,” and so on. And if you’re a college student, and you don’t know what a power of 2 is, I have to say: shame on you, you should know this stuff already. But it’s OK: it’s not complicated, and I’ll tell you how it works. 2 to the so-many power is just a 1 multiplied by that many 2’s. So a 2 to the power of 2 (“2 to the second power”) is 1 times 2 2’s: 22 = 1 x 2 x 2 = 4 . 2 to the power of 3 (“2 to the third power”) is 1 multiplied by 3 2’s: 23 = 1 x 2 x 2 x 2 = 8 . 2 to the power of 4 (“2 to the fourth power”) is 1 multiplied by 4 2’s: 24 = 1 x 2 x 2 x 2 x 2 = 16 . And so on. “Why is it 1 times that many numbers?” I’ll tell you why: because that way, 20 (“2 to the zero power” – I don’t think “zeroth” is really a word) comes out to be just 1: 20 = 1 x (no 2’s) = 1 . And mathematically, that’s exactly right: any (finite) number to the zero power equals 1. Want some more? OK, a piece of jargon: the number, which 2 is “to the power to,” is called an “exponent”. So in the case of 23, 3 is the exponent. |
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