# Question: Simplify Fraction with Powers

## Comment on Simplify Fraction with Powers

### Hey Brent!

Hey Brent!
What is wrong with this approach:
breaking up to ((6*4)^5 . (4*3)^3)/(6^6 . (4*4)^4 which turned out to be 9/6=3/2 ### Hi Abrahamic01,

Hi Abrahamic01,

The first part of your solution looks good: ((6*4)^5 * (4*3)^3)/(6^6)*(4*4)^4

I'd have to see the rest of your calculations, to see how you arrived at the answer of 3/2

### Hi Brent,

Hi Brent,
http://www.beatthegmat.com/correct-ordering-t276893.html
In this question, when it says "If x is positive", it tells me right away that I need to test integer and none integer positive values, so I tested 2, 3 and 1/2, but it didn't come to my mind to test another fraction like what you did when you tested 3/4.
My question is, how you decide what values to choose to test, does it have anything to do with the sense, I mean, as you are expert and specialized in math, so by experience the suitable values will jump to your mind or how?
Because the question looks easy, but if I don't test the right values, I will end up choose the wrong answer.
Thanks. Since there are 3 possible orderings, we should be prepared to plug in at least 3 sets of values.

However, as you have noted, it's hard to tell which values to plug in (other than an integer value and a fractional value).

If x = 3/4 had not yielded a "nice" result (i.e., identifying another possible ordering), I would have tried a couple more different values.

This highlights the shortcomings of plugging in numbers.

As you can see, Mitch's post (below my post at the linked question above) uses a different approach that relies on CRITICAL POINTS to help determine the correct answer.

In the following article, I write about the shortcomings of plugging in answer choices with respect to Data Sufficiency questions, but I think it applies here as well: https://www.gmatprepnow.com/articles/data-sufficiency-when-plug-values

### (6^5.4^5)x(4^3.3^3)/6^6x(4^4

(6^5)(4^5)x(4^3)(3^3)/6^6x(4^4)(4^4)
(6^5)(4^8)(3^3)/(6^6)(4^8)
(6^-1)(3^3)
(1/6)(3^3)= 9/6 = 3/2

whats wrong with this approach? 