Theory of Indices. 33 



Second, let n=—r, a negative quantity, either integral or frac- 

 tional, then 



b-"" a"- \a\ ~ b ~\b\ 

 a 



EXAMPI^ES. 

 I. Write the following expressions, using fractional ex- 

 ponents in place of the radical signs : 



^^ a^x 



3 fi_ 6 Wf 



2. Write the following expressions, using radical signs in 

 place of fractional exponents : 



Multiply ^ " ^ by jrt 

 2. _ .3 



Multiply x'^ hy X '\ 



Multiply ~ by -^. 

 x^^ x~^ 



Multiply j^^P'' by -^. 



5 

 6 



7 

 8 



9 

 10 

 II 

 12 



14. 



ix) 



Divide Tf +j/M)y_ r-r+j'/^ 



11 ill 



Divide :^—xjr-\-x^y~y" by ,r^— y^ 



I- ii i .1. 



Divide x'^ -j-jy'^ by .r-+jj/-. 



i il 8. 1 i_ 



Multiply X- —x''^ -}-x- —x^- -\-x'^ —x-\-x^—i by.v-"+i. 



Simplify \x'--^x'\ '\ 



( 1 1)2 

 Simplify \x^j~':^^ 



Find the continued product of 



