PPT: Exponents and Power | Mathematics (Maths) Class 8 PDF Download

 Page 1


Power Play
Page 2


Power Play
Exponential Notation
Exponential notation is a shorthand way of writing repeated multiplication of the 
same number.
Examples:
n × n = n² ³ read as "n squared" or "n raised to the 
power 2"
n × n × n = n³ ³ read as "n cubed" or "n raised to the 
power 3"
n × n × n × n × n × n × n = nw ³ "n raised to the power 7"
In general: n _ means you are multiplying n by itself a times.
Page 3


Power Play
Exponential Notation
Exponential notation is a shorthand way of writing repeated multiplication of the 
same number.
Examples:
n × n = n² ³ read as "n squared" or "n raised to the 
power 2"
n × n × n = n³ ³ read as "n cubed" or "n raised to the 
power 3"
n × n × n × n × n × n × n = nw ³ "n raised to the power 7"
In general: n _ means you are multiplying n by itself a times.
Using Letters (Algebra) in Exponential Form
When letters are multiplied, we can also use exponents:
a × a × a × b × b
= a³ × b²
This is read as "a cubed times b squared"
a × a × b × b × b × b
= a² × bt
This is read as "a squared times b raised to the power 4"
So, each letter is multiplied by itself the number of times shown in the exponent.
It9s important not to confuse addition with exponents:
4 + 4 + 4 = 3 × 4 = 12 ³ This is repeated addition
4 × 4 × 4 = 4³ = 64 ³ This is repeated multiplication
Page 4


Power Play
Exponential Notation
Exponential notation is a shorthand way of writing repeated multiplication of the 
same number.
Examples:
n × n = n² ³ read as "n squared" or "n raised to the 
power 2"
n × n × n = n³ ³ read as "n cubed" or "n raised to the 
power 3"
n × n × n × n × n × n × n = nw ³ "n raised to the power 7"
In general: n _ means you are multiplying n by itself a times.
Using Letters (Algebra) in Exponential Form
When letters are multiplied, we can also use exponents:
a × a × a × b × b
= a³ × b²
This is read as "a cubed times b squared"
a × a × b × b × b × b
= a² × bt
This is read as "a squared times b raised to the power 4"
So, each letter is multiplied by itself the number of times shown in the exponent.
It9s important not to confuse addition with exponents:
4 + 4 + 4 = 3 × 4 = 12 ³ This is repeated addition
4 × 4 × 4 = 4³ = 64 ³ This is repeated multiplication
Prime Factorisation Using Exponents
Any number can be written as a product of prime factors in exponential form .
Example:
Writing in Exponential Form
Now we group the same prime numbers and use exponent s to show how many times each is 
used:
2 × 2 × 2 × 2 = 2t
3 × 3 × 3 × 3 = 3t
5 × 5 = 5²
So, in exponential form:
32400 = 2t × 3t × 5²
Page 5


Power Play
Exponential Notation
Exponential notation is a shorthand way of writing repeated multiplication of the 
same number.
Examples:
n × n = n² ³ read as "n squared" or "n raised to the 
power 2"
n × n × n = n³ ³ read as "n cubed" or "n raised to the 
power 3"
n × n × n × n × n × n × n = nw ³ "n raised to the power 7"
In general: n _ means you are multiplying n by itself a times.
Using Letters (Algebra) in Exponential Form
When letters are multiplied, we can also use exponents:
a × a × a × b × b
= a³ × b²
This is read as "a cubed times b squared"
a × a × b × b × b × b
= a² × bt
This is read as "a squared times b raised to the power 4"
So, each letter is multiplied by itself the number of times shown in the exponent.
It9s important not to confuse addition with exponents:
4 + 4 + 4 = 3 × 4 = 12 ³ This is repeated addition
4 × 4 × 4 = 4³ = 64 ³ This is repeated multiplication
Prime Factorisation Using Exponents
Any number can be written as a product of prime factors in exponential form .
Example:
Writing in Exponential Form
Now we group the same prime numbers and use exponent s to show how many times each is 
used:
2 × 2 × 2 × 2 = 2t
3 × 3 × 3 × 3 = 3t
5 × 5 = 5²
So, in exponential form:
32400 = 2t × 3t × 5²
Multiplying Powers with Same Base
Multiplication Rule
n ×
a
n =
b
n
a + b
Example: 2 ×
3
2 =
4
2 =
3 + 4
2
7
Division Rule
n ÷
a
n =
b
n
a 2 b
Example: 5 ÷
7
5 =
3
5
4