Question

把数字 $2, 0, 2$ 和 $3$ 填入下列表达式中，每个方框放一个数字。这个表达式的最大可能值是多少？

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?

$0$

$8$

$9$

$16$

$18$

Click to load, then click again to play

不要把 $0$ 放在底数位置，因为那会让这个因子等于 $0$ 。

所以 $0$ 必须放在指数位置。指数为 $0$ 的那一项会自动等于 $1$ 。

为了让这项尽量小，应该使用 $2^0$ 。

剩下另一项可以是 $2^3$ 或 $3^2$ 。显然 $3^2$ 更大。

于是最大值为 $2^0 \times 3^2 = 1 \times 9 = 9.$

所以正确答案是 C。

Note that we do not want $0$ as a base, since that would make the expression equal to $0.$

This means that $0$ must be an exponent. The number whose exponent is $0$ will automatically evaluate to $1.$

Therefore, we should minimize this number, so we can put $2^0.$

Now the other term is $2^3$ or $3^2.$ Clearly, $3^2$ is larger, so we should use that.

This gives us a final value of $2^0 \times 3^2 = 1 \times 9 = 9.$

Thus, C is the correct answer.