# What are Exponents in Maths? - Grade 7 Maths Questions With Detailed Solutions

What are exponents in maths? Grade 7 maths examples and algebra questions are presented along with detailed solutions. Detailed Solutions and explanations are included.

## What are an exponents in maths and where are they used?

Examples: Exponents in maths 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)

1. 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
2. Evaluate the following:
a) 2 4
b) 10 4
c) (-2) 4
d) -2 4
3. 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
4. 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
5. Detailed Solutions and explanations are included.