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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