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2014 Math Kangaroo

Problem 3

Problem 3 · 2014 Math Kangaroo Easy
Algebra & Patterns substitution

How big is the value of \(a^{-3k}\), if \(a^k=\dfrac{1}{2}\)?

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Answer: B — 8
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Hint 1 of 2
You are not asked for a, only for a power of a^k.
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Hint 2 of 2
Write a^{-3k} using the quantity a^k that you already know.
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Approach: rewrite the unknown power in terms of a^k
  1. Note a^{-3k} = (a^k)^{-3}.
  2. Since a^k = 1/2, this is (1/2)^{-3} = 2^3 = 8.
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