Understanding Positive and Negative Exponents

numbers2So you may be in algebra or algebra II, and be introduced to negative exponents. Here’s a good way of understanding how they work. When you have an exponent, like b^x, where b is the base, you can split b into b*1, since all numbers are itself times one, this may make it easier to understand. Then b^x means you have 1 times a series of multiplications of b’s x long. So that’s why b^x, where x is zero, is 1: you have a 1with no b’s being multiplied; if x is 1 you have 1 times one b, which equals b; b^2=1*b*b, and so on. Now, if x is negative, that means you have 1 being divided by a series of a multiplication of b’s x long. So b^-1 equals 1/b, b^-2 equals 1/(b^2), and so on.

Photo by Stewf
internal tag: math

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