Problem 4 · 2013 Math Kangaroo
Easy
Algebra & Patterns
place-value
What is the value of the cube root of \(3^{(3^{3})}\)? (Note: \(a^{b^{c}}\) means \(a^{(b^{c})}\).)
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Answer: D — \(3^{3^{2}}\)
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Hint 1 of 2
First read the tower: 3 raised to (3 to the 3rd).
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Hint 2 of 2
Taking a cube root divides the exponent by 3.
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Approach: exponent arithmetic
- 3^(3^3) = 3^27.
- Its cube root is 3^(27/3) = 3^9.
- Since 9 = 3², this equals 3^(3²), which is choice D.
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