M 



Algebra. 



!9. Formula (a) may be used when either or both of the ex- 

 ponents are negative if the above interpretation be correct. 

 I^irsf, suppose r=—q, then 



But by substituting in the formula, 



a"a~'^=a"~'^, 

 Second, suppose 7i=—g, then 



a'' 

 But by substituting in the formula, 



so that formula (a) may be used when n is negative. 

 Third, suppose 7i=—s and r=—q, then 

 _^ -?_ ^ ^ _ ^ _ ^ 



But by substituting in the formula, 



so that formula (a) may be used where both 7i and r are 

 negative. 



20. Formula (b) may be used when either 7i or r or both are 

 negative. 



First, suppose r negative and equal to —q, then 



I _ I 

 (a")'~aJ~ 

 But by substitution in the formula, 



so that formula (b) may be used when r is negative. 

 Second, suppose 7i negative and equal to —q, then 



But by substituting in the formula, 



SO that fonnula (b) may be used when n is negative. 



(^")' /.«W/ ^nr 



