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Advanced Math/Quotient of two powers with the same base

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Question
Math Problem 1
Math Problem 1  
Hi, I am having difficulty understanding the answer to the attached image. I corrected the problem during class but did not have enough time to understand how the answer was gotten.

Answer
This problem uses fairly simple algebraic laws for exponents. As an example, for arbitrary numbers a, n and m

(a^n)(a^m) = a^(n+m)   <--- add exponents when multiplying

(a^n) / (a^m) = a^(n-m)     <--- subtract exponents when dividing

You can rearrange the expression to line up the a's and b's to make it look more like the above. Also, note that

3/9 = 3/(3^2) = 3^(1-2) = 3^(-1) = 1/3.

Randy

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randy patton

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college mathematics, applied math, advanced calculus, complex analysis, linear and abstract algebra, probability theory, signal processing, undergraduate physics, physical oceanography

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26 years as a professional scientist conducting academic quality research on mostly classified projects involving math/physics modeling and simulation, data analysis and signal processing, instrument development; often ocean related

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J. Physical Oceanography, 1984 "A Numerical Model for Low-Frequency Equatorial Dynamics", with M. Cane

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M.S. MIT Physical Oceanography, B.S. UC Berkeley Applied Math

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