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2023 Math Kangaroo

Problem 8

Problem 8 · 2023 Math Kangaroo Medium
Arithmetic & Operations order-of-operations

What is the value of the following sum? \(2^{0^{2^3}} + 0^{2^{3^2}} + 2^{3^{2^0}} + 3^{2^{0^2}}\)

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Answer: D — 12
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Hint 1 of 2
Evaluate each tower of exponents from the top down.
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Hint 2 of 2
Remember 0 raised to a positive power is 0, and anything to the 0 power is 1.
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Approach: evaluate each power tower carefully
  1. First term: 2(0^...) = 20 = 1. Second term: 0(positive) = 0.
  2. Third term: 2(3^1) = 23 = 8. Fourth term: 3(2^0) = 31 = 3.
  3. Sum = 1 + 0 + 8 + 3 = 12.
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