Theory of Indices. 



29 



29. Examination of formula (b). 



As before, let - and ^ be any two positive fractions, and 

 71 q 



— ^ and — - any two negative fractions. Then there are four 

 11 q 



cases to consider. 



First, U" = what? 



First case. 



{ Jll 



.•: from (6) and (-]) \a" j " =a"\ 

 and by direct substitution in the formula we also get 



Second case. 



ta« 



"1- 



= «"^. 



1 r.^L~ '■±~^ ""' 

 \a" i ^ a"f 



and by direct substitution in the formula we also get 



Third case. 





I I "^ " 



a" \ 





