What are an exponents in math and where are they used?
Examples: Exponents in math are used
a) To represent A repeated multiplication of a number by itself as shown below.
.
For example, 5 × 5 × 5 may be written as 5^{ 3}.
Hence 5 × 5 × 5 = 5^{ 3}, 5 is called the base and 3 is the exponent or power.
b) To represent large numbers in more simplified form.
Example: 100,000 = 10 × 10 × 10 × 10 × 10 = 10^{ 5}
c) To represent small numbers in more simplified form.
Example: 0.00001 = 1 / 100,000 = 1 / 10^{ 5}= 10^{ 5}
d) To write units of area.
The area of a square of side 1 meter is : 1 meter × 1 meter = (1 × 1)(meter × meters)
= 1 meters^{ 2}
(read "meters^{ 2}" as meters squared, unit of area)
e) To write units of volume.
The volume of a cube of side 1 meters is : 1 meter × 1 meter × 1 meter
= (1 × 1 × 1)(meter × meters × meters)
= 1 meter^{ 3}
(read "meters^{ 3}" as meters cubed, unit of volume)
f) To represent prefixes used with units of measures such as grams, meters,....
Kilo means 1000 = 10^{ 3}
example: 1 kilogram = 10^{ 3} grams = 1000 grams
Mega means 1000,000 = 10^{ 6}
example: 1 megabytes = 10^{ 6} bytes = 1000,000 bytes
Giga means 1000,000,000 = 10^{ 9}
example: 1 gigabytes = 10^{ 9} bytes = 1000,000,000 bytes
Solve the following exponents problems.(Solutions and explanations included)

Write the following using exponents:
a) 8 × 8 × 8 × 8
b) 10 × 10 × 10 × 10 × 10 × 10 × 10
c) A × A × A
d) meter × meter
e) centimeter × centimeter × centimeter

Evaluate the following:
a) 2^{ 4}
b) 10^{ 4}
c) (2)^{ 4}
d) 2^{ 4}

Use exponents to write the following using one power only.
a) 4 × 8
b) 25 × 5
c) 16 × 4 × 4^{ 3}
d) 2 × 2 × 8 × 2^{ 3}
e) B × B × B^{ 3}

Use exponents to rewrite the following expressions in simplified forms.
a) 2^{ 3} × 2^{ 4}
b) 6 × 6^{ 3}
c) 5 × 5^{ 2} × 5^{ 3}
Detailed Solutions and explanations are included.

