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## Official Guide Explanation:Problem Solving #46

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: 46
Page: 158
Difficulty: 4 (Moderately Easy)
Category 1: Arithmetic > Powers and Roots of Numbers > Powers
Category 2: Arithmetic > Fractions >
Category 3: Arithmetic > Decimals >

Explanation: Exponent rules are crucial on problems like this. When the same number is raised to different exponents in the numerator and denominator of a fraction, subtract the exponents. Here, it looks like this: (((0.3)5)/((0.3)3)) = (0.3)(5 - 3) = (0.3)2 = 0.09, choice (C). If you find multiplying decimals particularly error - prone, you can always switch to fractions at the second to last step: (0.3)2 = ( (3/10))2 = (9/100) = 0.09.

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