Problem 1 · 2013 Math Kangaroo
Easy
Arithmetic & Operations
estimate-and-pick
Which of the following numbers is the biggest?
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Answer: C — \(20^{13}\)
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Hint 1 of 2
Compare the sizes by how fast each grows, not by computing them all.
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Hint 2 of 2
An exponent stacked on a base of 20 dwarfs a small power or a plain product.
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Approach: compare orders of magnitude
- The plain product 20·13 = 260 and 201³ are modest next to a tower with exponent 13.
- 2^13 = 8192, but 20^13 multiplies thirteen copies of 20, vastly more than thirteen copies of 2.
- 20^13 has far more digits than any other choice, so it is the biggest: C.
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