26 Algebra. 



exampi.ks. 

 I. Write — T, 111 one li^^e. 



p. Write .^ in one line. 



?. Wnte " m one line. 



^ I 



d. Write " "^^ all in the /^rc'<:r line. 



A X~^ V~'' ">'" 



5. Write - 1,^ r so that all exponents are preceded by 



the + sign. 



6. Write ~ — - — with all positive exponents. 



23. Having now dispensed with formula (d) and extended 

 formulas (a), (b), (c) so that the exponents may be any ivholc 

 munbers, positive or negative, the question arises, can we give still 

 greater generality to our formulas by using exponents which are 

 fractions ? 



24. If quantities with fractional exponents have any meaning 

 and if we can use them in our formulas, we must have by form- 

 ula (b) 



11 being here a7iy positive ivhole number; i. e. a" is a quantity 

 which raised to the nth power equals a. 



A »/- 



Raise both sides of this equation to the 7'th power, r being a 

 positive whole number, and we get 



\a^\ = {Va)" 



so that, if we are permitted to use fractional exponents, a>' denotes 

 the /-th power of the ;^th root of a. 



