Exponents – Multiplying and Dividing Exponents

By Stuart Ackerman

     Exponents, also known as powers, are a shorter way of expressing a number multiplied by itself. 
 
For example, 5³ is 5 times itself 3 times, or 5 x 5 x 5 =125
 
The way to express 5³ out loud is to say either 'five to the third power' or '5 cubed'.
When a fraction such as ¾ is raised to an exponent power, both numerator and denominator get raised to that power.
 
For example ¾²      = 3 x 3 = 9
                                     4 x 4 = 16
 

Multiplying Exponents
If we wanted to multiply 4³ by 4² we would first write them out:
 
4³ = 4 x 4 x 4, and 4²= 4 x 4, so 4³ x  4² = 4 x 4 x 4 x 4 x 4
 
There are 5 fours, so we would have 4 to the power of 5.  There is a simple way to figure this out without writing all of this down.
 
The rule is: When multiplying exponents with the same base, just add the exponents.
 
In the above example, both exponents had the same base of 4.

4 x 4 x 4 x 4 x 4

 4 x 4

Two of the fours on the bottom cancel out with two of the fours on the top.  So, there are 3 fours left on the top.

When dividing exponents, the rule is: When you divide exponents with the same base, subtract the exponents.

It is important to remember to write out the exponent (e.g. For 5³ we would write 5 x 5 x 5) before multiplying or dividing exponents.

 ©Tutorgiant.com