Exponents
(KS3, Year 7)

An exponent tells you how many times a number (or other quantity) is multiplied by itself.

Understanding Exponents

It is easier to understand exponents with an example. Imagine we wanted to multiply 3 by itself 2 times. We would write 3 with a small 2 written to the right and above it: 3².

Powers, Bases and Exponents

• A power is the product of multiplying a number by itself. 3² is equal to 3 multiplied by itself 2 times, which equals 9.
• 3 is called the base. It is the number that is multiplying itself.
• 2 is called the exponent. It tells you how many times the base is multiplying itself.

Real Examples of an Exponent

Some real examples of exponents are given below.

• The power below has an exponent of 3:
  
  
• The power below has an exponent of 4:
  
  
• The exponent can also be a letter. The power below has an exponent of n:
  
  

Negative Exponents

Exponents can also be a negative number. A negative exponent tells you how many times to divide 1 by the number. For example, 3⁻² means divide 1 by 3, 2 times:

A negative exponent means put the base under 1 (or turn it upside-down if the base is a fraction), and make the exponent positive.
how to find a negative exponent

Fractional Exponents

An exponent can be a fraction. A fractional exponent means finding a root of a number. For example, 3^½ means the square root of 3:

Exponents, Powers and Indices

An exponent can also be called a power or an index (plural indices).

Saying an Exponent

How do you say 3²? You could say:

• 3 to the power of 2.
• The second power of 2.
• 3 to the 2.
• In the special case where the exponent is 2, we can say 3 "squared".

Note: In the special case where the exponent is 3, as in 3³, we can say 3 "cubed".

The Laws of Exponents

There are several laws of exponents, which are very useful in algebra. We use these laws when we are multiplying and dividing bases with exponents. They also help us understand negative and fractional exponents.
the laws of exponents

An Exponent of 1

If a number or a letter does not have an exponent, imagine it has an invisible exponent of 1:

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