Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Till now, I have encountered this kind of problem several times. Am I right to assume that these are the rules for simplifiying expontents like those in the questions:

\(2^k=2*2^{k-1}\) I can simplify from k to k-1. \(2^{k+1}=2*2^k\). I can simplify from k+1 to k

BUT I CAN'T simplify the first equation "backwards" meaning that if I see a exponent like \(5^{k-1}\) I have to see directly that I have to get all other exponents to k-1??

I hope you get my question :D Thanks for your help

Till now, I have encountered this kind of problem several times. Am I right to assume that these are the rules for simplifiying expontents like those in the questions:

\(2^k=2*2^{k-1}\) I can simplify from k to k-1. \(2^{k+1}=2*2^k\). I can simplify from k+1 to k

BUT I CAN'T simplify the first equation "backwards" meaning that if I see a exponent like \(5^{k-1}\) I have to see directly that I have to get all other exponents to k-1??

I hope you get my question :D Thanks for your help

Greetings!

What you need to do in any question depends on that particular question.

You know that \(2^k=2*2^{k-1}\) so you can easily get \(2^k\) down to \(2^{k-1}\). Also, \(2^{k-1} = 2^k/2\). So whether you bring the terms down to (k-1) or (k) depends on the question. Here all options involve multiplication. Hence you will need to use \(2^k=2*2^{k-1}\).
_________________

Till now, I have encountered this kind of problem several times. Am I right to assume that these are the rules for simplifiying expontents like those in the questions:

\(2^k=2*2^{k-1}\) I can simplify from k to k-1. \(2^{k+1}=2*2^k\). I can simplify from k+1 to k

BUT I CAN'T simplify the first equation "backwards" meaning that if I see a exponent like \(5^{k-1}\) I have to see directly that I have to get all other exponents to k-1??

I hope you get my question :D Thanks for your help

Greetings!

No, you could also change \(5^{k-1}\) to \(\frac{5^{k}}{5}\) It is a bit more complicated but may help to understand.

In this case, you would get \(2^{k}*5^{k-1} = \frac{2^{k} * 5^{k}}{5} = \frac{10^{k}}{5} = \frac{10*10^{k-1}}{5} = 2*10^{k-1}\)
_________________

Thank You = 1 Kudos B.Sc., International Production Engineering and Management M.Sc. mult., European Master in Management Candidate

Re: Which of the following is equal to (2^k)(5^k − 1)? [#permalink]

Show Tags

12 Aug 2015, 17:20

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________