QC - a < 0 < b

[tobias.apps]

a < 0 < b

Quantity A: a^-10
Quantity B: b^-5

I selected B since a positive is always going to be greater than a negative, no matter how large. The answer is D but I can't find where the two quantities either equal each other or quantity B is smaller than A.

Neither can be zero, and when they are both equal to 1 or -1, the resultant quantities are 1 and -1.

[nazmul.2000]

a < 0 < b

Quantity A: a^-10
Quantity B: b^-5

let a=-1; -1/2
b=1; 1/2
so A= (-1)^-10 =1/((-1)^10) =1 similarly for -1/2 u will get a different +ve no. The important thing is that for A u will always get a +ve result as the power is even.

& B= 1^-5 = 1/(1^5) =1
& so on...
So the ans is D.

[tommywallach]

Hey Tobias,

Here are some things to keep in mind when doing a question like this.

1) Isn't B a little bit too obvious? If the whole question were just about whether a positive to a power or a negative to a power is bigger, wouldn't that be a little too easy?

2) Remember that it isn't enough to only think about 0 and 1. Consider all these categories when trying to prove D:

Zero
One or Negative One
Fractions
Negative Fractions
Extreme (very large/very small numbers)

Only when you're really considered all of these (conceptually at least--you don't need to plug all of them in) can you feel confident in your answer.

3) Remember this question is about exponents, and fractions and negatives do weird things with exponents.

4) Don't set the two things "equal" (in this case, 1 and -1, or 2 and -2) unless the question tells you you have to! You can try that once, but then make sure you also try numbers where they're different.

Good luck!

-t