# 5.2a - 9/24/2008 Exponentials as repeated multiplication 25...

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9/24/2008 1 Exponentials as repeated multiplication 2 5 = 2 2 2 2 2 ( 5 2’s, multiplied) x n = x x x x x… x ( n x’s, multiplied) An abstract idea that you can understand: exponentiation is repeated multiplication, just as multiplication is repeated addition. Exponentiation is to multiplication as multiplication is to addition. Math-speak: x n ; Computer-speak: x^n A word about number sets The preceding definition assumes that the exponents are natural numbers (1,2,3, …) As we go along, we will extend the idea of exponents to negative numbers and even fraction (rational numbers). Right now, let’s focus on natural number exponents. Multiplying the same base to different exponents means “ n x’s times m x’s” how many x’s are there in all? n+m This give us the rule: x n x m = x n+m Try it on your calculator: 7^3 * 7^6, and compare to 7^9 also enter 7^(3+6) and compare to 7^3+6 Raising an exponential to another

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## This note was uploaded on 10/24/2010 for the course MATH MATH099 taught by Professor Jonh during the Spring '06 term at Pierce College.

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5.2a - 9/24/2008 Exponentials as repeated multiplication 25...

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