Page 65 - Maths On the GO Class 7

5 Exponents

Look at the following facts : Here, a is the base and n is the exponent or power or
index. It is read as ‘a to the power n’ or ‘a raised to the
Mass of the Uranus
power n’.
= 86,800,000,000,000,000,000,000,000 kg
Let us have a look on some more examples :
Mass of the Earth
4
2 2 2 2´ ´ ´ =2 ‘2 to the power 4’
= 5,972,000,000,000,000,000,000,000 kg
´
(–5) (–5) (–5) =(– ) 3 ‘–5 to the power 3’
´
5
Are you able to read these numbers comfortably? Of
course not. These are very large numbers and 1 1 1 1 1 1 æ ö 6 1
1
difficult to read, write and understand. So, to make ´ ´ ´ ´ ´ = ç ÷ ‘ to the power 6’
4 4 4 4 4 4 è ø 4
4
these large numbers easy to read, write and
understand, we use exponents.
Exponents
û In exponential form, base and exponent
When a number is multiplied by itself several times,
cannot be interchanged.
it can be written in short form called the exponential
û A negative rational number raised to an
form.
even power is positive.
For example : û A negative rational number raised to an
odd power is negative.
Product form Exponential Read as
p
form û If is any rational number and n is any
q
3 3 3 3 3 3 5 3 to the power 5 integer, then
´
´
´
´
or 3 raised to p n p n
q
the power 5. ( ) = q n
8 8 8 8 8 7 8 to the power 7
´
´
´
´ ´ ´8 or 8 raised to
8
8
the power 7. Solved Examples
In the exponential form, the number which is Ex am ple : Write the base and exponent for each of
repeatedly multiplied is called the base and the the fol low ing :
number of times it is repeated is called the exponent (a) 5 9 (b) (-100 ) 12
or index or power.
5
5
So, in the exponential form 3 , 3 is the base and 5 is (c) (2 2´ ) 5 (d) ç æ -3 ö
÷
the exponent. è 8 ø
7
Similarly in 8 , 8 is the base and 7 is the exponent. So lu tion :
In general, if a is any rational number and n is a (a) In 5 , base =5 and exponent =9
9
n
positive integer, then a a a´ ´ ´ … a (n times) = a .
Exponents 65