EIV : Chapter 2 : Problem Set #4

[johnnyboa]

If u is a positive integer, which of the following could be a negative number?

A) u^7-u^6
B) u^3+u^4+u^5
C) u^-9
D) u^-13+u^13
E) u^3-u^8

OA=E

I would like to believe that I have a good understanding of exponential properties but for some reason, I'm puzzled at how the answer is derived. I reasoned that odd exponents will result in a positive number, and even exponents can result in either a positive/negative number. So if the variable u is positive to begin with, then how come E is the answer and not A? I would appreciate any help. Thank you...

[JonathanSchneider]

You might want to revisit your exponent rules. Odd exponents will leave a product with the same sign as the base, whereas even exponents will leave a product that is positive. So, we can say that even exponents hide pos/neg solutions. However, this is when we are told that the product is positive, and we are trying to find the base.

In this case, we are told that the base is positive, and we are trying to find out about the product. As a result, you have to think about it in reverse. Because the base is an integer, it could be: 1, 2, 3... All exponential values will yield positive products (though some of those will be less than one). To get a negative, we must pick the answer choice that subtracts a potentially large product from a smaller one.