Exponents - what do they mean?

Exponents are a short cut to express certain types of multiplication. In algebra we sometimes want to multiply a number by itself again, and again, and again. If we wanted to write 8x8, we are multiplying 8 twice.  We would express this as the number 8 raised to the 2nd power.

The number 8 is called the base and the exponent is called the power.






Here are other examples:

When we see a number with an exponent, the exponent is telling us how many times to write the base.  We can use exponents on bases that are numbers or letters (variables).





Some practice problems to make sure you understand the concept:

Write the following using exponent form:

1. X*X*X*X*X

2. 3*3*3*a*a

3. 6*6*X*X*Y*Y*Y

Write the following exponents out to show the expanded form (indicating where multiplication is occurring):

4. 3m⁴n<sup>6

5. 22x4y3

6. 23mn3p2 

Solutions:</sup>

1. X⁵

       2. 3³a²     

       3. 6²X²Y³

4. 3*m*m*m*m*n*n*n*n*n*n
5. 2*2*x*x*x*x*y*y*y
6. 2*2*m*n*n*n*p*p

Here is a link to a short, but useful video explaining how exponents work (click here) - check it out if you need a little more explanation.