SOLUTION: {{{((u^(3/4))(u^(1/3)))/((u^(2/3))(u^(5/6)))}}}=u^(a/b) where a=? and b=12

Algebra ->  Square-cubic-other-roots -> SOLUTION: {{{((u^(3/4))(u^(1/3)))/((u^(2/3))(u^(5/6)))}}}=u^(a/b) where a=? and b=12      Log On


   

Question 14462: =u^(a/b) where a=? and b=12
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
Given that
=u%5E%28a%2Fb%29,
we have to find the value of a when b=12
The formulae we use here are
1.a%5Em%2Aa%5En=a%5E%28m%2Bn%29
2.%28a%5Em%2F%28a%5En%29%29=a%5E%28m-n%29 and
3.If a%5E%28p%2Fq%29=a%5E%28r%2Fs%29, then %28p%2Fq%29=%28r%2Fs%29
Using the first 2 formulae we simplify the left hand side of given equation as



=u%5E%28%283%2F4%29%2B%281%2F3%29-%282%2F3%29-%285%2F6%29%29

=u%5E%28%283%2A3%2B1%2A4-2%2A4-5%2A2%29%2F12%29=u%5E%28-5%2F12%29

Hence we have LHS=u%5E%28-5%2F12%29=RHS
=u%5E%28a%2Fb%29
Now using the third formula , we have
-5%2F12%29=a%2Fb%29
Since it is given that b=12,substituting in the above ,we get
a=-5