Theory of Indices. 17 



r o ' 



i^. Multiply I — by ;f *. 



r I V 



75. Multiply I - , a} and <2 together. 



r 1 1 ^ 



7<5. Multiply - hy x\ 



ly. Multiply ^^ by jit 3. 



ZfS*. Multiply x^, 2^ and x^ together. 



J p. Multiply x^ by (2x)^. 



20. Multiply 3^ ^^, 2^ and ^t:^ together. 



P7. Multiply TS-^/ by (^2j;j^ 



^^. Multiply (2,x)^ by (^2-rj^ 



^j. Multiply f 3-r/ by (^2Jt:j^ 



.?^. Multiply (2)X)^ by (^2Ji:j^ 



^5. Multiply (^xf by (^2J>:j^ Compare with example 2t. 



26. Multiply ( — zxf by (2x)^. 



2y. Multiply (x-\-y)'^ by (x-\-yy. 



28. Multiply (x—yf by (x—y)\ 



2g. Multiply (x—yf by (x-\-y)'^. 



JO. Multiply (x^—y), (x—y)^ and (x'\-y)^ together. 



31. Find the value of [«("+''']"+^ 



j2. Distinguish between a^"^^ and (a")'' 



7. To find the quotient of two powers of the same quantity. 



^ a^ aaa 



a^ aa ' 



aaaaa 

 and a5_j_^3__. _^^__^2_ 



aaa 

 In each of these two cases the quotient is seen to be a with an 

 exponent equal to the exponent of the dividend mi7ius the ex- 

 ponent of the divisor. 



aa I 



Again, a'-h-a^=' =-, 



^ aaa a 



aaa i 



and «3_i.^5__ = 



aaaaa a^ 



In each of these two cases the quotient is seen to be a fraction 

 whose numerator is i and whose denominator is a with an ex- 

 ponent equal to the exponent of the divisor viiiiiis the exponent 

 of the dividend. 



