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1. 
 Made by :- Paritosh Malik
 Class :- 7
 Section :- B
 Submitted to :- Mrs Annu Ma’am
Maths FA-2 Project

2. Very large quantities like planetary masses and very small
distances like atomic sizes are very difficult to comprehend
and compare without the use of exponents.
Examples :- 625=5*5*5*5=52
343=7*7*7=73

3. 
We can expand numbers by using factorization and
write them as exponents with different bases :-
729=3*3*3*3*3*3=36
72=2*2*2*3*3=23*32
2 4 2 * 2 * 2 * 2 16
3 3 * 3 * 3 * 3 81
Conversion into Power
Notation

4. The following laws of exponents are very
useful to do operations of multiplication and
division in numbers involving exponents.

5. 
If (x) is a rational number and (a) and (b) are whole
numbers then :-
xa*xb=xa+b
Examples :- 33*34=(3*3*3)*(3*3*3*3)=37
We can get the same result using the law given:
33*34=33+4=37
Law : 1

6. 
If (x) is a rational number and (a) and (b) are the any whole
,then :-
xa/xb = xa-b
27/23 = 2*2*2*2*2*2*2 = 24
2*2*2
We can get the same result using the law given above :-
27/23 = 27-3 = 24
Law : 2

7. 
If (x) is a rational number and (a) and (b) are whole
numbers ,then :-
(xa)b = xab
(32)4 = 32* 32* 32* 32 = 32+2+2+2 = 38
We can get the same result using the law given above
:-
(32)4 = 32*4 = 38
Law : 3

8. 
If (x) is rational number other than zero ,then x0=1.
x3/x3 = x3-3 = x0 (Using Law 2) and
x3 / x3 = x*x*x = 1 or x0 = 1
x*x*x
Thus we arrive at the law given above.
Law : 4

9. If (a) and (b) are rational numbers and (m) is any whole number
,then :-
am * bm =(ab)m
32 * 42 = 3*3*4*4
= (3*4)*(3*4)
= (3*4)2 = 122
Law : 5

10. 
If (a) and (b) are rational numbers and (m) is any whole
number ,then :-
am a m
bm b
32 / 32 = 32 = 3*3 = 3 3 = 3 2
52 = 5*5 = 5 5 5
Law : 6
=

11. 
This notation is very helpful to express very large
numbers or very small numbers.
Any number can be expressed in scientific notation in
the form (k)*10n where (k) is equal to one or more than
one but less than ten and n is an integer.
Scientific Notation

12. 
The distance between the Earth and the Moon is about 370,000
km. If we have to express this in scientific notation.
Step 1 :- Convert the large number into a decimal number, where
the decimal is placed after the firs non-zero digit.
Example of Scientific
Notation
3 7 0 0 0 0
370000 km = 3.70000 * 100000 km