Algebra Indices and surds                        

       

KEY POINTS Definition : for n integer and a  0, a n  a  a  a...  a (n factors ) a1  a and a 0  1 (a is called the base) Multiplication

: a n  a p  a n p

Division

: an  a p  n

1  n a

an  a n p p a a and   b

Negative index

: a

Power of a power

:  a n   a n p

n

b   a

n

p

1 n

Fractional index

: a  a

Different bases

: a  b   ab  n

n

n p

a  an 

and

n

n

p

an  a  and n    b b

 a p

n

n

 

KEY POINTS Definition

: for a  0, a is the positive number so that

Multiplication

:

2

a

ab  a  b a2  a  a 

in particular

 a

 a

2

a

( for a  0)

a a  ( for a  0, b  0) b b Difference of squares :  x  y  x  y   x 2  y 2 Division

:

hence



a b





a  b  a b

a  b is called the conjugate (expression) to a  b Rationalise the denominator: 

b a b a a    b b b b

a b 1 1 a b    a b a b a b a b (Multiple numerator and denominator by the conjugate expression)

