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## Comment on

Fractional Exponents## Please help me with this one.

Is 3^(a²/b) < 1 ?

(1) a < 0

(2) b < 0

## TARGET QUESTION: Is 3^(a²/b)

TARGET QUESTION: Is 3^(a²/b) < 1 ?

This is a great candidate for REPHRASING the target question. Notice that, if order for 3^k < 1, it must be the case that k < 0.

So, in order for 3^(a²/b) < 1, it must be the case that a²/b < 0 (i.e,, a²/b must be negative). So, let's REPHRASE our target question as....

REPHRASED TARGET QUESTION: Is a²/b < 0?

STATEMENT 1: (1) a < 0

There are several values a and b that satisfy statement 1. Here are two:

CASE A: a = -1 and b = -1. In this case a²/b = (-1)²/(-1) = -1. Here, a²/b < 0

CASE B: a = -1 and b = 1. In this case a²/b = (-1)²/(1) = 1. Here, a²/b > 0

Since we cannot answer the REPHRASED TARGET QUESTION with certainty,

statement 1 is NOT sufficient.

STATEMENT 2: b < 0

There are several values a and b that satisfy statement 2. Here are two:

CASE A: a = 1 and b = -1. In this case a²/b = (1)²/(-1) = -1. Here, a²/b < 0

CASE B: a = 0 and b = -1. In this case a²/b = (0)²/(-1) = 0. Here, a²/b = 0 (in other words, a²/b is NOT less than 0)

Since we cannot answer the REPHRASED TARGET QUESTION with certainty,

statement 2 is NOT sufficient.

STATEMENTS 1 and 2 COMBINED

If a < 0, then a CANNOT equal 0, which means a² is POSITIVE

If b < 0, then b is NEGATIVE

So, a²/b = POSITIVE/NEGATIVE = NEGATIVE

In other words, a²/b < 0

Since we can answer the REPHRASED TARGET QUESTION with certainty, the combined statements are sufficient.

Answer: C

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