AMC8 2011

AMC8 2011 · Q15

AMC8 2011 · Q15. It mainly tests Exponents & radicals, Primes & prime factorization.

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

$4^5 \cdot 5^{10}$的乘积有几位数？

(A) 8 8

(B) 9 9

(D) 11 11

(E) 15 15

Answer

Correct choice: (D)

正确答案：（D）

Solution

\[4^5 \cdot 5^{10} = 2^{10} \cdot 5^{10} = 10^{10}.\] That is one $1$ followed by ten $0$'s, which is $\boxed{\textbf{(D)}\ 11}$ digits.

$\[4^5 \cdot 5^{10} = 2^{10} \cdot 5^{10} = 10^{10}.\]$ 这是一个1后面跟着十個0，总共$\boxed{\textbf{(D)}\ 11}$位数。

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