Here 2 is called the base and 6 is called the power (or index or exponent).
We say that "64 is equal to base 2 raised to the power 6".
Similarly, if m is a positive integer and 
a
a
…m times = am.Laws of Indices
If m and n are positive integers, and
then
an = am + n [Product Law]
(ii)
[Quotient Law]
(iv) (ab)m = am . bm
(v)
(vi) ao = 1
(vii)
Surd
An irrational root of a positive rational number is called a surd. Consider a number with base 'a' as a positive rational number with power of a fraction, say
then
Since
is an nth root, it is called a surd of order n, if it is irrational.
is a surd of order 3.
(ii)
is a surd of order 2.
is NOT a surd because
and 3 is NOT an irrational number.

(i) 36-1/2 (ii) 
(i) 36-1/2
= (62)-1/2 = 6-1





(i) 
(iii) Simplify: 
(v) Show that (xp - q)p + q (xq - r)q + r (xr - s)r+s = 1
(vi) 49
7x = (343)2x - 5 find 'x'.


2
2
2
2
2
2
= 27
We have 2x+2 = 27 [
bases are equal ]
x + 2 = 7 [
powers are equal ]
x = 5
(iii) 

= (x3a y6)1/4
(x2/3 y-1)a 
x2a/3 y-a [
(x3a)1/4 = x3a/4 (power law)]

(v) LHS = x(p - q) (p + q) x(q - r) (q + r) x(r - s) (r +s)

(vi) 49
7x = (343)2x - 5
72
7x = (73)2x - 5
72+x = 76x - 15
2 + x = 6x - 15

