42 Algebra. 



expressing the radical b}' means of fractional exponents and then 

 reducing them to a common denominator, Thus 



x^'^4Xn/3Xn/2 = 4V2* 



= 4^- 2>'^ 2''' (by Art. 8)= ' ^ 4-^x 3^X 2^=2 V108. 

 Also -' J_5';'_i5 l5'__^i Vs-V^ 



19. Examples. Find the value of each of the following ex- 

 pressions : 



/. '^ 3<2<:X ^ 2a7n X s^bax. 



2. N/|x>/|xN/i. 



3. s/ixx^'^i- 



4. a^s/ a — xy^x'^'^ a-\-x. 



5- ^ TO X ^ TT- 



6. 2A^'^X3.r". 

 .S'. '?'24X6v/3. 



/O. 



2v/6-T-6'v^ 2. 





•^ a-—x^-^s/ a- 



J5- 5^^3- 



16. -- 



v« — ji' >/a-\-x 



A polynomial involving radicals is generally more easily multi- 

 plied or divided by another such polynomial by first expressing 

 the radicals by fractional exponents. As shown in Chapter II, 

 the work will then be no different in principle from the case when 

 the exponents are integral. But in a few of the simpler instances 

 it is unnecessary^ to pass to fractional exponents, e. g. 



