Exponents
Exponents can make your math problems a lot easier to handle.
Simply put, it is a shortcut for multiplying numbers over and over again.
Look at the following multiplication problem:
8 × 8 × 8 × 8 × 8 × 8
Instead of multiplying 8 six times by itself,we can just write 8
^{6} and it will mean the same thing.
When reading 8
^{6}, we say eight to the sixth power or eight to the power of six.
In a similar way,
12 × 12 × 12 × 12 × 12 × 12 × 12 × 12 × 12 × 12 = 12
^{10}
In 12
^{10}, 12 is called the base and 10 is called the exponent
Other examples:
5
^{3} = 5 × 5 × 5
9
^{4} = 9 × 9 × 9 × 9
7
^{2} = 7 × 7
6
^{6} = 6 × 6 × 6 × 6 × 6 × 6 × 6
2
^{8} = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
In general,
y
^{n} = y × y × y × y ×...× y × y (n times)
In our example above, it says 7
^{2} = 7 × 7
What would you say 7
^{1} is equal to?
For 7
^{2}, you wrote down 7 twice
Therefore, for 7
^{1}, you will write down 7 once and of course there is not need to have a multiplication sign
7
^{1} = 7
Common pitfalls to avoid when working with exponents:
What is 2
^{6} equals to?
Is it equal to 2 × 2 × 2 × 2 × 2 × 2 ?
Or is it equal to (2 × 2 × 2 × 2 × 2 × 2) ?
It is equal to (2 × 2 × 2 × 2 × 2 × 2) = (2
^{6}) =  64
However, (2)
^{6} is a different story
(2)
^{6} = (2) × (2) × (2) × (2) × (2) × (2) =  ×  ×  ×  ×  ×  × 2 × 2 × 2 × 2 × 2 × 2
Notice that  ×  = +
So,  ×  ×  ×  ×  ×  × 2 × 2 × 2 × 2 × 2 × 2 = + × + × + × 2
^{6}
+ × + = +
+ 2
^{6}
In (2)
^{6}, the exponent is even. Change it to any odd number and the answer will be negative
(2)
^{7} = (2) × (2) × (2) × (2) × (2) × (2)× (2) =  ×  ×  ×  ×  ×  ×  × 2 × 2 × 2 × 2 × 2 × 2 × 2
 ×  ×  ×  ×  ×  ×  × 2 × 2 × 2 × 2 × 2 × 2 × 2 = + × + × + ×  × 2
^{7}
+ × + × + ×  × 2
^{7} = + ×  × 2
^{7}
+ ×  = 
+ ×  × 2
^{7} = 2
^{7}
Observation:
a
^{n} is always negative
(a)
^{n} is either negative or positive. It is positive is an is an even number. It is negative if n is an odd number
a
^{n} is not always equal to (a)
^{n}
a
^{n} is equal to (a)
^{n} only when n is an odd number
What if the base is a fraction?
When the base is a fraction it is common to use to use parentheses as shown below:
The above is also equal to
8
/
27
Exponents quiz to check your understanding of this lesson.

Jul 28, 17 02:38 PM
Bessy has 6 times as much money as Bob, but when each earn $6. Bessy will have 3 times as much money as Bob. How much does each have before and after
Read More
New math lessons
Your email is safe with us. We will only use it to inform you about new math lessons.