Theory of Indices, 

 examples. 



1. Divide x^ by x^. 



2. Divide jt^ by jr^. 



J. Divide (—x)^ by (—x)\ 



4.. Divide —x^ by —x^. 



5. Divide —x^ by (—x)^. 



6. Divide —x* by (—x)'". 



7. Divide (—x)^ by (—x)^. 



S. Divide [-'l^''yf' 



Q. Divide I — 



J L ^ 



by -| 



J^o. Divide (x—y)^ by 



--Tj 



zz. Divide (x—y)^ by 



J^^. Divide (x^—y^)^ by T-^— j/. 



zj. Multiply b^ by ^^ and divide the product by b\ 



14. Divide b^ by b^ and multiply the quotient by b^. 



75. Divide b^ by b^ and multiply the quotient by b^. 



16. Multiply b^ by b"" and divide the product by b\ 



ly. Divide b^ by b"^ and multiply the quotient by b-. 



18. Divide b^ by b^ and multiply the quotient by b^. 



19. Multiply b"^ by b^ and divide the product b)^ b^. 



20. Divide b'' by b^ and multiply the quotient by b^. 



21. Divide b^ by b^ and multiply the quotient by b^. 



22. Divide c'' by c^, the quotient by c^ and so on until five 

 divisions are performed. 



23. Divide c^ by c^, the quotient by c^, and so on until five 

 divisions are performed. 



10. We saw that a"^a''=a"~'' xin^r. Now let us take ;'=i, 

 then {n being a positive whole number) when we divide a" by a 

 we simply subtract one from the exponent. 



Now let us take some number for w, say 5, and divide a> b}' a, 

 the quotient by a, and so on as long as we can, each time per- 

 forming the division by subtracting one from the exponent. 



