Question: Crazy Exponents

Comment on Crazy Exponents

Why does "n" being simply positive make "2n" even?
greenlight-admin's picture

This even/odd concept has nothing to do with a number being positive or negative.
The important/crucial information here is that n is an integer. The definition of an "even integer" says that, if x is an even integer, then x = 2k for some integer k.
So, for example, we know that 14 is even, because we can write 14 = 2(7), and 7 is an integer.
Likewise, -6 is even, because we can write -6 = 2(-3), and -3 is an integer.
Also, 0 is even, because we can write 0 = 2(0), and 0 is an integer.
So, since we're told that n is an integer, we can be certain that 2n is even

this course is always helpful thanks for questions like this

In the beginning, how did you get 2n+3? If we're adding n, shouldn't it be 2+n+3?
greenlight-admin's picture

Yes, we do add the exponents.
So, (x^n)[x^(n+3)] = x^(n + n+3) = x^(2n + 3)

Likewise, [x^(2n+1)][x^(8n+5)] = x^(2n+1 + 8n+5) = x^(10n + 6)

Hello, with 25 days left on my prep, what steps should I be taking in order to perform well on the GRE? I am only on the power roots module. Do you recommend utilizing other sources such a Manhattan 5 lb book? To sum up what I am asking, how should I prepare being on a time constraint of 25 days? Thank you!!
greenlight-admin's picture

My answer to your question depends on your responses to the following questions:

1) How much time you can study each day?
2) What are your target scores?
3) At what level are your present abilities? To answer this last question, it helps to have taken a practice test.

That said, you can always follow our step-by-step Study Guide: https://www.greenlighttestprep.com/study-guide/overview

ASIDE: You probably won't need any additional resources beyond this course. We have tons of practice questions.

1. I can devote on average 18 hours per week studying due to work and other activities.
2. My target scores are 150 on math and verbal, so 50th percentile
3. I ve taken one practice test you recommended and got 148 verbal and 152 math however, I am starting to feel overwhelmed by the different concepts.

There are days during the weekend and some weekdays where I study much longer but are you saying your study guide can give me scores I desire? I seen others study guides that will vary on the subjects (magoosh) so I am confused to what I should follow. Thank you for your time.
greenlight-admin's picture

That information is very useful!

Since you're already scoring around your target scores, your job now is to identify and strengthen all remaining weaknesses.

My advice: The GRE is a test of your math and verbal skills, AND it's a test of your test-taking skills. So, taking several practice tests is an important part of your prep. This will help you build your test-taking skills, and it will help you identify any remaining area(s) of weakness.

While carefully analyzing your practice tests, there are four main types of weakness to watch out for:

1. specific Quant skills/concepts (e.g., algebra, geometry, etc.)

2. specific Verbal skills/concepts (e.g., vocabulary, 3-blank text completion questions, etc.)

3. test-taking skills (time management, endurance, anxiety etc.)

4. silly mistakes

For the first two weaknesses, the fix is pretty straightforward. Learn the concept/skill and find some practice questions to strengthen that weakness.

If your test-taking skills are holding you back, then you need to work on these. For example, we have a video about test anxiety at http://www.greenlighttestprep.com/module/general-gre-info-and-strategies...

Finally, if silly mistakes are hurting your score, then it's important that you identify and categorize these mistakes so that, during tests, you can easily spot situations in which you're prone to making errors. I write about this and other strategies in the following article: http://www.greenlighttestprep.com/articles/avoiding-silly-misteaks-gre

I hope that helps.

Cheers,
Brent

Dear Brent,

Thank you for these useful videos. I have noticed that, when you divide x to the power of 4n+6 to x to the power of 2n+5 you wrote the answer as x to the power of 2n+1. I do the same as rule says and my answer was 2n+11. Of course, it is not affect to the result. But however, can you explain why you wrote 2n+1?
greenlight-admin's picture

Glad to help!

When dividing powers with the same base, we subtract the exponents.

In general, (b^x)/(b^y) = b^(x-y)

So, to divide x^(4n+6) by x^(2n+5), we must subtract (2n+5) from (4n+6)

In other words, the new exponent will equal (4n+6) - (2n+5) [ASIDE: the brackets are VERY important here]

(4n+6) - (2n+5) = 4n + 6 - 2n - 5
= 2n + 1

Does that help?

Cheers,
Brent

What if n = 1.5 ? (which is a positive number)
(1.5 x 2) + 1 = 4
X to the Power of 4 must be a positive number.
Thank you!
greenlight-admin's picture

The only problem with your solution is that n must be an integer, and 1.5 isn't an integer.

Have a question about this video?

Post your question in the Comment section below, and a GRE expert will answer it as fast as humanly possible.

QC Strategies

When you encounter a Quantitative Comparison question, be sure to consider which strategy might best apply: 

 

Let me Know

Have a suggestion to make the course even better? Email us today!

Free “Question of the Day” emails!