# Lesson: Introduction to Exponents

## Comment on Introduction to Exponents

### Hey Brent,

Hey Brent,

regarding this Q with exponents and inequalities:

https://gmatclub.com/forum/gmat-diagnostic-test-question-79337.html

In the two statements, since I don´t know the sign I can´t simply divide or multiply. But can I do si if I consider the case of x being positive and x being neg.? It worked out for me on this one.

To be more specific:

Stmt 1: 1/x > -1

case 1 (x pos): -1<x
case 2 (x neg): 1<x

thus, insuff.

Stmt 2: 1/x^5>1/x^3

case 1 (x pos): 1>x
case 2 (x neg.): 1>x

thus, suff.

Is that possible? or did it luckily work out with the specific set of numbers in that particular Q? Without seeing your full solution, it's hard to tell whether the steps you took are valid.

That is, for Statement 2 you write:
case 1 (x pos): 1 > x
case 2 (x neg.): 1 > x
These are correct conclusions (for each case), but how did you arrive at those conclusions?

Cheers,
Brent

### I assumed two cases for the

I assumed two cases for the statement: Case 1 x being negative, so when I multiplied by x I switched the < and the other case assuming x being positive, so I miltiplied but didn´t switch the <.

However, I just noticed that when doing that for stmt 2 (which actually yields an answer), I get for assuming x being neg. and pos. respectively two contradicting results. So I guess my approach is invalid? ### Sorry, but I'm still not 100%

Sorry, but I'm still not 100% clear on your solution.
For statement 2, are you multiplying both sides by x or x^3 or x^5?
In the meantime, Bunuel provides a nice solution here: https://gmatclub.com/forum/gmat-diagnostic-test-question-79337-20.html#p...