Carcass wrote:
x is a positive, odd integer.
Quantity A |
Quantity B |
\((-3)^x\) |
\(-2^{2x}\) |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Two important rules:
ODD exponents preserve the sign of the base. So, (
NEGATIVE)^(
ODD integer) =
NEGATIVEand (
POSITIVE)^(
ODD integer) =
POSITIVEAn EVEN exponent always yields a positive result (unless the base = 0)
So, (
NEGATIVE)^(
EVEN integer) =
POSITIVEand (
POSITIVE)^(
EVEN integer) =
POSITIVEWe're told that x is a positive, ODD integer
So, \((-3)^x = (-3)^{ODD} = (NEGATIVE)^{ODD} = NEGATIVE\)
Conversely, if x in a integer, we know that 2x is EVEN
So, \(-2^{2x} = -2^{EVEN} = (NEGATIVE)^{EVEN} = POSITIVE\)
We get:
QUANTITY A: Some NEGATIVE number
QUANTITY B: Some POSITIVE number
Answer: B
Cheers,
Brent
_________________
Brent Hanneson – Creator of greenlighttestprep.com
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