一道GWDTN20的数学题求解

ziningxiao

The operation x&n for all positive integers n greater than 1 is defined in the following manner: x&n = x raised to the power of x&(n-1). If x&1 = x, which of the following expressions has the greatest value?

• A(3&2)&2
• B3&(1&3)
• C(2&3)&2
• D2&(2&3)
• E(2&2)&3
  

我当时来不及做，想着n的大小是关键。在一个表达式里面&后边的部分是关键，所以选了D，答案也是D
但是，我不太理解 x&n = x raised to the power of x&(n-1). If x&1 = x的幂的运算是怎么运作的
求解啊

小怡儿

&原来是幂的意思哇？那我猜猜，他给的x与n的关系式是不是给你举个例子，x乘以x的n-1次幂等于x的n次幂，同理x&1=x也是举例子？那选项就是先算括号里面的幂运算，在把它当做整体看。比如A的话就是3的平方是9，算9的平方为81.D先算2的3次方为8，再算2的8次方，就是256咯？

quanquan0525

碰巧在考GMAT上看到的
x&1 = x

x&2 = x raised to the power of x&1 (which is just x), so x&2 = xx = x^x (we’ll use the caret symbol ^ to represent exponentiation, since as we’ll see, we’re going to do it a lot!)

x&3 = x raised to the power of x&2, so x&3 = x^(x^x)

x&4 = x^(x^(x^x))

So the number after the & sign tells you how many x’s are in the exponential expression. Now we can translate the answer choices. As always, do the operation inside the parentheses first.

(A) (3&2)&2

quanquan0525

底数是2的还是没有底数是3的大呢