Page 32 - Maths Skills - 8

30 Maths

INTRODUCTION
We know about the exponential notation of natural numbers. The integral exponents of a rational number and the
laws of exponents of rational numbers are the main topic of this chapter. We shall study the scientific notation of
large and small numbers also. But before we start, let us have a quick review of those which have studied in the
earlier classes.
Let’s Review

We know that 2 × 2 × 2 × 2 × 2 × 2 can be written as 2 and read as two raised to the power six or as the sixth
6
power of two. In 2 , the integer 2 is called the base and 6 is called the exponent (index).
6
Similarly, in (– 4) , the base is – 4 and the exponent is 2. The notation for writing the product of an integer
2
multiplied by itself several times is called the exponential notation or power notation.

INTEGRAL EXPONENTS OF A RATIONAL NUMBER
The product of a rational number multiplied several times by itself can also be expressed in the exponential
notation.
3 3 3 3 3 3 3 6 3
For example; × × × × × can be written as , where is called the base and 6 is called the
5
5
5
5
5
5
5
exponent. 5
p p n p n
Rule: If q is any rational number and n is a positive integer, then q q n

Thus, p 3 p p p ppp p 3 , Fact-o-meter

q q q q qqq q 3 n n
p q
4
q
p

p p p p p pppp p 4
, and so on.

q q q q q qqqq q 4
LAWS OF EXPONENTS
p
Let q be any rational number and ‘m’ and ‘n’ be any integers then, we have :
 p m  p n  p mn+  p m  p n  p mn−
1.   ×   =   2.   ÷   =   when m > n

q 

q 
q 


q 
q 


q 
   p  n  p mn  p r n  p n n  p r n  p n n

m
r  
r  
3.     =   4.  ×  =   ×   and  ÷  =   ÷  
   q     q   q s  q   s   q s  q   s 
1  p − n  q  n
5. p = 6.   =  
–m
p m  q   p
 p 0
7.   =1 8. (–1) odd number = –1 9. (–1) even number = +1
q 

10. ()p 0 1 , p 11. n p = () and n p = () m n
p
1
p
m
0
n