Carcass wrote:
x is a positive, odd integer.
Quantity A |
Quantity B |
\((-3)^x\) |
\(-2^{2x}\) |
The important thing to remember here is that the negative sign in front of \(-2^{2x}\) tells us to take the value of \(2^{2x}\) and then multiply it by \(-1\)
So, we can say that \(-2^{2x}=-(2^{2x})\)
Given:
QUANTITY A: \((-3)^x\)
QUANTITY B: \(-(2^{2x})\)
Useful property (aka Power of a Power law): \((b^x)^y = b^{xy}\) Let's apply this property in reverse to rewrite Quantity B as follows:
QUANTITY A: \((-3)^x\)
QUANTITY B: \(-[(2^2)^x]\)
Simplify Quantity B:
QUANTITY A: \((-3)^x\)
QUANTITY B: \(-(4^x)\)
Rewrite Quantity A as follows:
QUANTITY A: \([(-1)(3)]^x\)
QUANTITY B: \(-(4^x)\)
Apply the Power of a Product Law to get:
QUANTITY A: \((-1)^x(3^x)\)
QUANTITY B: \(-(4^x)\)
We are told that x is an ODD integer, we know that \((-1)^x\) preserves its sign.
In other words, \((-1)^x = -1\)
So we can write:
QUANTITY A: \(-(3^x)\)
QUANTITY B: \(-(4^x)\)
For every positive integer x, we know that \(3^x < 4^x\)
So, we can also conclude that, for every positive integer x, \(-(3^x) > -(4^x)\)
Answer: A
Cheers,
Brent
_________________
Brent Hanneson – Creator of greenlighttestprep.com
If you enjoy my solutions, you'll like my GRE prep course.
Sign up for GRE Question of the Day emails