sandy wrote:
\(-(x)^3 = 64\)
Quantity A |
Quantity B |
\(x^4\) |
\(x^5\) |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
GIVEN: -(x)³ = 64
In other words: (-1)(x)³ = 64
Divide both sides by -1 to get: In other words: x³ = -64
KEY PROPERTY:
ODD exponents PRESERVE the sign of the base. That is, POSITIVE^ODD = POSITIVE and NEGATIVE^ODD = NEGATIVE
For example, (-2)^5 = -32 and 2^5 = 32
Conversely,
EVEN exponents result in values are greater than or equal to zero. (-2)^6 = 64, 5^4 = 625, etc
So, once we know that x³ = -64, we know that
x is NEGATIVE So, we get:
Quantity A:
NEGATIVE^4
Quantity B:
NEGATIVE^5
If we applies the above
properties, we get:
Quantity A: POSITIVE
Quantity B: NEGATIVE
Answer: A
Cheers,
Brent
_________________
Brent Hanneson - founder of Greenlight Test Prep