Difference between revisions of "2011 AMC 8 Problems/Problem 15"

Revision as of 16:06, 21 November 2022

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 x 5^10 has a total of 7+4, 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

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 ==Solution 2==
-<cmath>4^5 has four digits while 5^{10} has 7 digits. This means that </cmath>4^5 \cdot 5^{10} has a total of 7+4, 11 digits.
+^5 has 4 digits while 5^10 has 7 digits. This means that 4^5 x 5^10 has a total of 7+4, 11 digits.
 ==See Also==
 {{AMC8 box|year=2011|num-b=14|num-a=16}}
 {{MAA Notice}}