28 Algebra. 



First, a" a"^ = what ? 

 Second, a" a '^= what? 

 Third, 07^0^= what? 

 Fourth, a "a '/= v/hat? 



and b}' direct substitution in the formula we get 



a'^a'' =a"^ '' 

 Second case. 



a" a ''' = a"^a "f= j <2"'^ a'"' ] 



= 1^"^ J = ^ "'/ = ^^/■?^^j 2L=«" " . d^ 



and b}^ direct substitution in th? formula wc also get 



a" a '^=a" ''' 



Third case. 



This is the same as the second case, only the order of the fac- 

 tors is changed, and therefore as in the second case the result will 

 be the same as given by direct substitution in the formula. 



Fourth case. 



--^-^11 I 



a "a -= ^-/= ,. ^ 



a'' a'^ a" a'f 

 = --— ^=« '"'■/' = a " '' 



and by direct substitution in the formula we also get 



' ■ n " 'I - 



C 



Thus we see that by using fractional exJponents according to 

 the suggestions before obtained, the result of multiplying two 

 fractional powers of a is, in every case, in perfect accord with for- 

 mula (a). 



