Melody

For how many positive integers n > 1 is it true that 2^{24}*2^{36} is a perfect nth power?

2^60, (2^2)^30, (2^3)^20, (2^4)^15, (2^5)^12, (2^6)^10, (2^10)^6, (2^12)^5, (2^15)^4. (2^20)^3, (2^30)^2

You can count.

Answered on the earlier version.

Next time please refer people to the earlier post in your question.

Thanks for the address guest:

Let the amount he has to start with be x where x >=200

She puts $50 in her left pocket leaving x-50 remaining.

She gives away 2/3(x-50) leaving 1/3(x-50) to go into her right pocket.

So now she has  50+1/3(x-50)

We are told that this is more than x-200

and you can finish it.

Great idea Dennis, be rude to a senior member. 

Show that you have no interest in actually learning anything.

That will get you a lot of worthwhile help in life.   

Yay, way to go Dennis! 

Your way was not easier or more sensible. If you think about it you will work that out.

I just looked at each term in the first bracket and saw what I could pair it with from the second bracket.

Each of the 5 terms only had at most one pair, that is how it always must be.

By convention, the answers MUST be positive.

Come on, you can work this out!

1000=3^x

3,9,27,81,243,729, too big

6

the total number of numbers is 9*9!

The total number starting with an even and having each consecutive pair adding to an odd is  4*4!*5!

The total number starting with an odd and having each consecutive pair adding to an odd is  5!*5!

\(Prob=\frac{4*4!*5!+5!*5!}{9*9!}\\ Prob=\frac{5!4!(4+5)}{9*9!}\\ Prob=\frac{5!4!}{9!}\\ Prob=\frac{2*3*4}{6*7*8*9}\\ Prob=\frac{1}{6*7*3}\\ Prob=\frac{1}{126}\\\)

Hi Jenny,

Q1

Start with sin(3x)=sin(2x+x)

Do the expansion and just keep expanding what you get until it all falls out.

Give it a go and come back with what you have done.