Problem 5 · 2022 Math Kangaroo
Medium
Number Theory
factorization
\(5^8\) pencils are distributed evenly among 25 empty boxes. How many pencils are in each box?
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Answer: A — \(25^3\)
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Hint 1 of 3
Write the number of boxes, 25, as a power of 5 before dividing.
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Hint 2 of 3
Divide \(5^8\) by \(5^2\) using the rule \(5^m/5^n=5^{m-n}\).
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Hint 3 of 3
Then rewrite the answer as a power of 25 to match the choices.
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Approach: turn 25 into a power of 5 and subtract exponents
- There are \(25=5^2\) boxes, so each box holds \(5^8/5^2=5^6\) pencils.
- Rewrite \(5^6=(5^2)^3=25^3\).
- Each box holds \(25^3\), choice A.
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