algebraic indicies (1 Viewer)

[tristambrown]

Hey all

just posting to ask for your help with the simplification of a q i am working on.

i have the solution infront of me, i just cant see why it works (as i dont have a very good math background)

I have correctly gotten the solution down to:

n!(n-5)!5!*3^(n-5)
------------------------- = 1
n!(n-4)!4!*3^(n-4)

I can see how in the next step the n! will cancel but am having trouble seeing how the 3^(n-x) parts cancel

According to the solution the next line should be

(n-5)!5!*3
------------- = 1
(n-4)!4!


So essentially my question is: how is it possible for the 3^(n-5)/3^(n-4)to cancel down to 3 rather than 3^(-1) ?

Thankyou very much in advance for your help with this - it's driving me mad.

 

[tristambrown]

Actually if someone could solve the above completley, indicating what was done and why, I would be greatly appreciative.

The worked solutions are impossible to follow as they skip how they get there :/

thanks again

 

[Riviet]

Well... it looks like the solutions are wrong in that line:

3^n-5 = 3^(n-5)-(n-4)
3^n-4

= 3^n-5-n+4
= 3^-1
= 1/3

So the next line should read:

(n-5)!5!
------------- = 1
(n-4)!4!*3

(n-5)(n-4)!*5*4!
------------------ = 1
(n-4)!*4!*3

5(n-5)=3
5n-25=3
5n=28
n=28/5

 

[tristambrown]

Thanks for that guys