AMC8 2023

AMC8 2023 · Q6

AMC8 2023 · Q6. It mainly tests Exponents & radicals, Fractions.

The digits $2,0,2,$ and $3$ are placed in the expression below, one digit per box. What is the maximum possible value of the expression?

数字 $2,0,2,$ 和 $3$ 被放置在下面的表达式中，每个方框一个数字。表达式的最大可能值是多少？

(A) 0 0

(B) 8 8

(D) 16 16

(E) 18 18

Answer

Correct choice: (C)

正确答案：（C）

Solution

First, let us consider the case where $0$ is a base: This would result in the entire expression being $0.$ Contrastingly, if $0$ is an exponent, we will get a value greater than $0.$ $3^2\times2^0=9$ is greater than $2^3\times2^0=8$ and $2^2\times3^0=4.$ Therefore, the answer is $\boxed{\textbf{(C) }9}.$

首先，考虑 $0$ 作为底数的情况：这将导致整个表达式为 $0$。相反，如果 $0$ 是指数，我们将得到大于 $0$ 的值。$3^2\times2^0=9$ 大于 $2^3\times2^0=8$ 和 $2^2\times3^0=4$。因此，答案是 $\boxed{\textbf{(C) }9}$。

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