Official Guide Explanation:
Problem Solving #216




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Solution and Metadata

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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