2011 AMC 8 Problems/Problem 15: Difference between revisions

Revision as of 10:05, 18 November 2024

How many digits are in the product $4^5 \cdot 5^{10}$ ?

$\textbf{(A) } 8 \qquad\textbf{(B) } 9 \qquad\textbf{(C) } 10 \qquad\textbf{(D) } 11 \qquad\textbf{(E) } 12$

$4^5 \cdot 5^{10} = 2^{10} \cdot 5^{10} = 10^{10}.$

That is one $1$ followed by ten $0$ 's, which is $\boxed{\textbf{(D)}\ 11}$ digits.

$4^5$ has $4$ digits while $5^{10}$ has $7$ digits. This means that $4^5 \cdot 5^{10}$ has a total of $7+4=\boxed{\textbf{(D)} 11}$ digits.

2011 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 14	Followed by Problem 16
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
All AJHSME/AMC 8 Problems and Solutions

@@ Line 19: / Line 19: @@
 ==Video Solution 1 by SpreadTheMathLove==
 https://www.youtube.com/watch?v=mYn6tNxrWBU
+==Video Solution by WhyMath==
+https://youtu.be/q7AUTz2i938
 ==See Also==
 {{AMC8 box|year=2011|num-b=14|num-a=16}}
 {{MAA Notice}}