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## Official Guide Explanation:Problem Solving #216

Background

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Review (12th ed.). Click the links on the question number, difficulty level, and categories to find explanations for other problems.

These are the same explanations that are featured in my "Guides to the Official Guide" PDF booklets. However, because of the limitations of HTML and cross-browser compatibility, some mathematical concepts, such as fractions and roots, do not display as clearly online.

Question: 216
Page: 183
Difficulty: 6 (Moderately Difficult)
Category 1: Arithmetic > Powers and Roots of Numbers > Powers
Category 2: Arithmetic > Fractions >

Explanation: Because the answer choices also have negative exponents, it's best to simplify without changing the sign of the exponents. (It might be easier to think of negative exponents as the reciprocals of their corresponding positive exponents, but it would waste a lot of time in this case.) Convert each of the three fractions to an exponent of (1/2): ((1/2))-3(((1/2))2)-2(((1/2))4)-1 = ( (1/2))-3((1/2))-4((1/2))-4 = ((1/2))(-3 + (-4) + (-4)) = ((1/2))-11, choice (B).

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