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Target question:What is the value of (8^a)(1/4)^b? This is a good candidate for rephrasing the target question.
Let's take (8^a)(1/4)^b and rewrite both parts with the same base of 2. Notice that 8 = 2^3 and 1/4 = 2^(-2) So, we can rewrite the original expression as: [(2^3)^ a][2^(-2)]^b Simplify to get: (2^3a)(2^-2b) [power of a power law] Combine terms to get: 2^(3a - 2b) To determine the value of 2^(3a - 2b), we must determine the value of (3a - 2b) So, let's rephrase the target question. REPHRASED target question:What is the value of 3a - 2b?
Statement 1: b = 1.5a Take: b = 1.5a Multiply both sides by 2 to get: 2b = 3a Subtract 2b from both sides to get: 3a - 2b = 0 PERFECT!! Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT
Statement 2: a = 2 Not enough info to determine the value of 3a - 2b Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT