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1991 AJHSME Problems/Problem 13

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Problem

How many zeros are at the end of the product 25\times 25\times 25\times 25\times 25\times 25\times 25\times 8\times 8\times 8?

\text{(A)}\ 3 \qquad \text{(B)}\ 6 \qquad \text{(C)}\ 9 \qquad \text{(D)}\ 10 \qquad \text{(E)}\ 12

Solution

\begin{align*}(5^2)^7\times (2^3)^3 &= 5^{14}\times 2^{9} \\&= 5^5\times 10^9 \end{align*} Since 5^5 doesn't end in a 0, we can conclude that the product ends in 9 zeroes \rightarrow \boxed{\text{C}}.

See Also

1991 AJHSME (Problems • Resources)
Preceded by
Problem 12 		Followed by
Problem 14
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
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Looking for a challenging algebra text? Preparing for MATHCOUNTS or the AMC exams?
Check out Art of Problem Solving's Introduction to Algebra by Richard Rusczyk.
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