To answer questions that involve negative fractions and exponents, you have to know the following rules:
1) Fraction with one in the numerator always obeys the following rule
1/High Number < 1/Low Number
What confuses test takers is the definition of High Number and Low Number when it comes to negative denominator
2) For negative numbers, remember this one rule
-5 < -3
- (Higher Positive Number) < - (Lower Positive Number)
3) When it comes to negative fraction, the rule reverses
-(1/High Number) > - (1/Low Number)
4) Even power of negative fraction is positive and odd power of negative fraction is negative
(-(a/b)) ^n is positive if n is even and negative is n is odd
Q) If a = -1/4 & b = -1/3, which of the following is true?
a) a^2 < b^3
b) a^3 > b^2
c) a^4 > b^6
d) a^3 < b^3
e) a^2 < b^4
Solution
Once you know the four rules, it becomes easier to eliminate answer choices. The question asks us to find the cube and square of two negative fractions a and b
a=-1/4 b=-1/3
According to Rule 3
a > b
If you look at the answer choices, a is represented as a^2 a^3 and a^4
And b is represented as b^2 b^3 b^4 , b^5 and b^6
Arrange the signs of the fraction, before solving it
a^2 = +
a^3 = -
a^4 = +
b^2 = +
b^3 = -
b^4 = +
b^5 = -
b^6 = +
Now eliminate answer choice based on signs
+ > -
Eliminate A, B and D
Answer Choices remaining C and D
c) a^4 > b^6
e) a^2 < b^4
Let us look at answer Choice D as both are relatively smaller powers
Solving e)
1/16 < 1/81
This is false. Hence, answer choice C is the Correct Answer. By adopting process of elimination techniques, you can avoid lengthy calculations.
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