31 8 ALGEBRA. 



2. Over the said quantities with their new indices 

 place the given index, and they will make the equivalent 

 quantities required. 



Note. A comnion index may also be found by reducing 

 the indices of the quantities to a common denominator, 

 and involving each of them to the power, denoted by it^ 

 numerator. 



EXAMPLES. 



I X 



T. Reduce 15 ^ and 9^ to equivalent quantities, having 



the common index ■-, 



•^-4-t~tXt=^=t the first index. 



^-7r~^=:^XY^i^==^y the second index, 



>■ i 



Therefore 15 ''I and 9' » are the quantities required. 



2. Reduce a^ and x'^ to the same common index 4-, 



•f-^|=:f Xf=|- the first index. 

 ■^--yrr-X-f^::^ the second index. 



— ^ TjT 



Therefore a^\^ and ^"^i are the quantities required, 



3. Reduce 3"" and 2^ to the common index -J. 



Ans. 2']^ and 4*^, 



4. Reduce «* and 3*^ to the common index |-. 



_^ Ans. ^[^ and Fi^. 



1. — 



5. Reduce a" and y" to the same radical sign. 



mn mn 



Ans. y/aP" and ^'b"". 



PROBLEM 



