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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

## I memorized all the square

Is there an easy way to quickly know this? Or another list that should be memorized for the GMAT?

## For cube roots, you must

For cube roots, you must recall the powers with exponent 3 (2³ = 8, 3³ = 27, 4³ = 64, 5³ = 125, etc)

So, for example, ∛64 = 4

For fourth roots, you must recall the powers with exponent 4

Cheers,

Brent

## Thanks for the comment! I am

## Hi Brent! Glad to post again

Regarding the following question

https://gmatclub.com/forum/if-m-4-1-2-4-1-3-4-1-4-then-the-value-of-m-is-93340.html

I understood the value of M like: 4^1/2 + 4^1/3 + 4^1/4. Looking for a common denominator I ended up with 4^13/12, which is a little bit more than 1 so, the value of M would be something more that 4. Hence, answer E. Is that approach correct?

warm regards,

Alejandro

## Question link: https:/

Question link: https://gmatclub.com/forum/if-m-4-1-2-4-1-3-4-1-4-then-the-value-of-m-is...

Even though you arrived at the correct answer, it was purely by coincidence.

The problem is that we can't add exponents the way you have. We can only add exponents when we're multiplying powers.

For example, (7^5)(7^10) = 7^15

When it comes to adding, however, there are no convenient simplifications.

For examples we can't say that 7^1 + 7^2 = 7^3

Cheers,

Brent

## Thanks for your words

## The beeth root... Love it!