t88 ALGEBRA, 



Thus, the quotient of ^^ divided by ^^ is a^""^, or a^c 

 That of ;v"by A;is.V'-\ 

 That of ^" by at" is x'''^ 

 That of ;v"^-^" by a;" is x'\ 

 And that of a;" by x*' is a;""''. 



But it is to be observed, that when the expoilent of the 

 divisor is greater than that of the dividend, the quotient 

 ■will have a negative exponent. 



Thus, the quotient of x^ divided by x'^ is x^""^, or x"^. 

 And that of ax^ by ^ ^ is ax"^. 



And these quotients, viz. x"^ and ax'~^y are respective- 

 ly equal to — - and — j ; for x^ being actually divided by 



X X 



' X^ 1 ax^ a 



«^ gives -y =~7 *, and aX divided by x^ gives •— ^zir-^ 



X X XX' 



as above. 



aX^ a 



In like manner, dx" divided by f;v *" gives — — zz - — . 



And the quotient of a* -^x* \ divided by «' -}"^' * I ^^ 



Moreover, aV divided by <2* gives a"^ ir^^=j. 



-rl ^ -'-- 



a-^xV divided by ^-j-AcI^ gives ^-[-^vl^ = 



«+Arp = ..+AiT 



And ah^x * I " divided by ^^ -j- ;r * T gives ah-^-x * | " . 



3CH0LIUM. 



