# GRE Test Question Homework: Is (n^*)^* = n?

• Xkaliber
In summary, the conversation is about evaluating the expression (n^*)^* and determining its relationship to n based on the given equation. The summary concludes that the two values are equal, where n^*=32-n and m^*=(32-n)^*.
Xkaliber

## Homework Statement

Hi,
I was doing some GRE practice tests and came across this question:

for all number n, $$n^*$$=32-n (apparently where the asterisk is an exponent)

They then give me two values, which are $$(n^*)^*$$ and n, and I am to say whether choice 1 is a greater value than choice 2, choice 2 is a greater value than choice 1, the two values are equal, or there is not enough info to determine. The answer key says they are equal. This means given the above equation, $$(n^*)^*$$ = n

I can't see how this is true... Anyone care to explain? Thanks

Let $n^*=32-n=m$. Then, $(n^*)^*=m^*$. Can you evaluate $m^*$?

cristo said:
Let $n^*=32-n=m$. Then, $(n^*)^*=m^*$. Can you evaluate $m^*$?

I'm not sure. Is there some way you want me to rewrite this? $m^*=(32-n)^*$

Xkaliber said:
I'm not sure. Is there some way you want me to rewrite this? $m^*=(32-n)^*$

Yes. The star is shorthand for the operation that "subtracts a given number from 32." In the case of $m^*$, the given number is 32-n. What is the result when you apply * to that?

lol, that was easy. I had in my mind that * was some sort of exponential value, not a more general operator. Thanks

## 1. What is the GRE Test Question Homework about?

The GRE Test Question Homework is a practice question on the GRE (Graduate Record Examination) which is a standardized test used for admission into graduate schools in the United States. This specific question is asking about a mathematical concept related to exponents.

## 2. What is the formula being tested in this question?

The formula being tested in this question is the power of a power property, which states that when raising a power to another power, the exponents are multiplied together. In this case, it is asking if (n^*)^* = n.

## 3. How can I solve this question?

This question can be solved by applying the power of a power property. When raising a power to another power, the exponents are multiplied together. Therefore, (n^*)^* = n^(*)* = n^(2*) = n^2.

## 4. Is this a common type of question on the GRE?

Yes, this is a common type of question on the GRE. The GRE tests mathematical concepts and skills, including exponents and their properties. It is important to have a strong understanding of these concepts in order to do well on the test.

## 5. Why is this question important for the GRE?

This question is important for the GRE because it tests the understanding of a fundamental mathematical concept. It also demonstrates the ability to apply this concept in a problem-solving situation. These skills are important for success in graduate school and in many careers.

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