Official Guide Explanation:
Problem Solving #166

Background

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Solution and Metadata

Question: 166
Page: 84
Difficulty: 6 (Moderately Difficult)
Category 1: Arithmetic > Powers and Roots of Numbers > Powers
Category 2: Algebra > Exponents >
Category 3: Arithmetic > Real Numbers >

Explanation: The -2 may be confusing for a moment, but recognize that the exponent it is raised to--2m--must be even. A negative integer raised to an even exponent will have a positive result, the same result as a positive number raised to the same exponent. Thus, we can rewrite the equation as:

2^2m = 2^{9 - m}

2m = 9 - m

3m = 9

m = 3, choice (C).

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