# Lesson: Negative Exponents

## Comment on Negative Exponents

### Here in the 3rd question, how

Here in the 3rd question, how do we know it is 3^(x+1). I actually interpreted it as (3^x)+1. Don't you think it is a bit confusing? The GRE Prep Club website has a few minor formatting issues when it comes to exponents. I agree, it's not 100% clear whether it's 3^(x+1) or 3^x + 1.

On test day, the notation will not be so ambiguous.

Cheers,
Brent

### What allows us to “flip each

What allows us to “flip each fraction “ in your process for the 3rd to last problem link? ### Hi Jay,

Hi Jay,

Are you referring to a question in the above video, or are you referring to one of the linked practice questions in the Reinforcement Activities box?

In general, we divide by a fraction by multiplying by its reciprocal.

For example, 1/2 ÷ 3/5 = 1/2 x 5/3
Also, 2/7 ÷ 11/5 = 2/7 x 5/11

Likewise, (2/3)/(7/11) = 2/3 ÷ 7/11 = 2/3 x 11/7

Does that help?

Cheers,
Brent

### Specifically I’m speaking of

Specifically I’m speaking of the 3rd to last reinforcement problem. I get multiplying by the reciprical for division of fractions, but I didn’t see the need for that in this problem, however when you described the process you said flip the equation and I was wondering how that was possible. Thanks as always

Jason We have the equation 5n/(4n - x) = 1/0.788

I wanted to apply the rule that says (a - b)/c = a/c - b/c
However, to apply this law, I needed to create an equivalent equation featuring a SINGLE expression in the denominator. That is, I wanted to rewrite 5n/(4n - x) as (4n - x)/5n

To accomplish this, I used the fact that, if two fractions are equal, then their reciprocals must also be equal.

That is, if x/y = a/b, then it must also be true that y/x = b/a (as long as none of the values is zero)

Does that help?

Cheers,
Brent

### https://greprepclub.com/forum

https://greprepclub.com/forum/if-5n-4n-x-8511.html

In this input type question, can I enter my answer in decimal form (0.06) if nothing is mentioned? Great question!

On the GRE, you will be told when to enter your response as a fraction. You will be given two boxes (one box for the numerator and one box for the denominator) to enter values. If there's just one box, then you can enter the value as a decimal.

When I first posted the question, I forgot to add directions to submit the answer as a fraction. I have now added text to that effect.

For more on how to enter values in Numeric Entry questions, watch 2:00 to 5:10 of the following video: https://www.greenlighttestprep.com/module/general-gre-info-and-strategie...

Cheers,
Brent

### t is an integer

t is an integer

Quantity A: 1/(1 + 2^t)
Quantity B: 1/(1 + 3^t)

We can solve this question using matching operations
Given:
Quantity A: 1/(1 + 2^t)
Quantity B: 1/(1 + 3^t)

Since 2^t is POSITIVE for all integer values of t, we know that 1 + 2^t is also POSITIVE
This means we can safely multiply both quantities by (1 + 2^t) to get:
Quantity A: 1
Quantity B: (1 + 2^t)/(1 + 3^t)

Likewise, since (1 + 3^t) is POSITIVE, we can safely multiply both quantities by (1 + 3^t) to get:
Quantity A: 1 + 3^t
Quantity B: 1 + 2^t

Subtract 1 from both quantities to get:
Quantity A: 3^t
Quantity B: 2^t

From here, we can TEST some integer values of t

If t = 0, we get:
Quantity A: 3^0 = 1
Quantity B: 2^0 = 1
In this case, the two quantities are EQUAL

If t = 1, we get:
Quantity A: 3^1 = 3
Quantity B: 2^1 = 2
In this case, Quantity A is GREATER

----------------------
In this question how do we know that 1/1+2^t is positive or negative? Since 2 is positive, we can conclude that 2^t is POSITIVE for all values of t

NOTE: Many students (incorrectly) believe that a NEGATIVE exponent results in a NEGATIVE value. This is not true.

For example, 2^(-1) = 1/2
2^(-2) = 1/4
2^(-3) = 1/8
2^(-4) = 1/16
etc

Since 2^t is always POSITIVE, we know that 1 + 2^t is POSITIVE, which means 1/(1 + 2^t) is POSITIVE

Does that help?

Cheers,
Brent

### In some questions we have the

In some questions we have the statement n is an integer so we assume that it is positive or negative? ### If n is an integer, then n

If n is an integer, then n can be negative, positive, or zero (which is neither positive nor negative)

Here are all the integers: {. . . . -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, . . . . }

Cheers
Brent

### Hi,in the following case are

Hi,in the following case are able to susbtract X in case both bases are the same?
https://greprepclub.com/forum/x-is-a-negative-integer-1895.html Sorry, can you elaborate? What part of the solution are you referring to?

### I meant the exponent

I meant the exponent

3 to the power of x+1 and 2 to the power of x

in both cases subtract -x so I will have 3 and 2,

will it be possible in the case that X is a positive integer? ### No, that strategy won't work.

No, that strategy won't work.

It's a perfectly valid strategy to subtract the SAME VALUE from each quantity, however that's not what you're going here.

Consider this example:
QUANTITY A: 3²
QUANTITY B: 5²

If we subtract the exponent 2 in both quantities, we aren't subtracting the SAME value from both quantities.
QUANTITY A becomes 3, which means we subtracted 6 from quantity A
QUANTITY B becomes 5, which means we subtracted 20 from quantity B

Does that help?

Cheers,
Brent

### In this case

In this case
https://greprepclub.com/forum/t-is-an-integer-9385.html

Given:
Quantity A: 1/(1 + 2^t)
Quantity B: 1/(1 + 3^t)

Since 2^t is POSITIVE for all integer values of t, we know that 1 + 2^t is also POSITIVE
This means we can safely multiply both quantities by (1 + 2^t) but in the case that instead of +2^t we have -2^t, we will not be able to multiply both quantities by (1 - 2^t)? because it will lead to different answers?
Thank you Yes, that's correct. Multiplying both quantities by a negative value will lead to a different answer.

### Hi Brent,

Hi Brent,

https://greprepclub.com/forum/if-5n-4n-x-8511.html
I tried solving this question using this approach:
5n/4n-x=1/0.788
= 0.788*5n=4n-x
= (788/1000)5n=4n-x
= 788n=200(4n-x)
= 788n=800n-200x
= -12n=-200x
= x/n=50/3

I am getting 50/3 instead of 3/50. Could you please point out where I am wrong.

Thanks,
Ketan ### You're soooooo close!!

You're soooooo close!!

Everything is correct to the point where you write: -12n = -200x
Now, divide both sides by n to get: -12 = -200x/n
Divide both sides by -200 to get: -12/-200 = x/n
Simplify to get: 3/50 = x/n

Cheers,
Brent

### I've noticed that questions

I've noticed that questions like: https://greprepclub.com/forum/x-y-and-p-are-integers-and-xyp-0-if-14322.html is one of my weak areas. I waver between trying numbers or reasoning through the question to save time but have had little luck. What if the second set of numbers you tried resulted in III being true? would you have tried another set of numbers? Isn't that time expensive? 