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2020/21 AHSMC Part 1 Problem 1

Problem 1 of 16

If 2a4b=16\dfrac{2^a}{4^b} = 16, then a−2ba - 2b is equal to

Answer choices

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Solution

Since 2a4b=2a22b=2a−2b\dfrac{2^a}{4^b} = \dfrac{2^a}{2^{2b}} = 2^{a-2b} and 16=2416 = 2^4, we have a−2b=4a - 2b = 4. The answer is (C).

University of Alberta