Infographics: Power Play | Mathematics Class 8- New NCERT (Ganita Prakash) PDF Download

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Exponents: Concepts, Laws, and 
Applications
What are Exponents?
Exponents represent repeated multiplication of a number by itself. If we have a base number and 
multiply it by itself a certain number of times, we use exponents to express this operation concisely.
a =
n
 
n times
 a × a × a × & × a
Where a is the base and n is the exponent (the power to which a is raised).
Examples
2 =
3
2 × 2 × 2 = 8
6 =
4
6 × 6 × 6 × 6 = 1296
10 =
7
10 × 10 × 10 × 10 × 10 × 10 × 10
Powers with Negative Exponents
Negative exponents represent the reciprocal of a number raised to a positive exponent:
a =
2 n
 
a
n
1
Examples
2 =
23
 =
2
3
1
 
8
1
5 =
22
 =
5
2
1
 
25
1
 = (
3
1
)
24
3 =
4
81
Laws of Exponents
1
Multiplication Law
a ×
m
a =
n
a
m+ n
2
Division Law
 =
a
n
a
m
a
m2 n
3
Power of a Power
( a ) =
m n
a
m n
4
Negative Exponent 
Law
a =
2 m
 
a
m
1
5
Zero Exponent Law
a =
0
1 ( a = à 0)
6
Product to a Power
( a b) =
m
a b
m m
7
Quotient to a Power
 = (
b
a
)
m
 
b
m
a
m
Standard Form of Numbers
A number is in standard form if it is written as:
m × 10 where 1 f
n
m < 10
Examples
3, 600, 000, 000, 000 = 3.6 × 10
12
0.00053 = 5.3 × 10
24
Comparing Numbers
When comparing large or small numbers in 
standard form, we first compare the exponents, 
then the coefficients if needed.
0.00024 = 2.4 × 10
24
0.000042 = 4.2 × 10
25
Since , we know  is smaller. 10 <
25
10
24
4.2 × 10
25