Free Algebra
Tutorials!
 
Try the Free Math Solver or Scroll down to Tutorials!

 

 

 

 

 

 

 

 
 
 
 
 
 
 
 
 

 

 

 
 
 
 
 
 
 
 
 

Please use this form if you would like
to have this math solver on your website,
free of charge.


Powers

If a is any number and n any positive integer (whole number ) then the product of a with itself n times, , is called a raised to the power n, and written a n ; i.e.,

The following important rules apply to powers.

We want these rules to be true for all positive values of a and all values of m and n:

We shall first look at the simpler cases.

Examples

(a) 10 2 × 10 3 = (10 × 10) × (10 × 10 × 10) = 10 5 = 10 2+3:

(b) 2 5 ÷ 2 3 = 32 ÷ 8 = 4 = 2 2 = 2 5-3

(c) ( 3 2 ) 3 = (3 × 3) 3 = (3 × 3) × (3 × 3) × (3 × 3) = 3 6 = 3 2 × 3

(d) From rule 2, a n + 1 ÷ a n = a ( n + 1) - n = a 1. Also,

(e) We have a n × a 0 = a n +0 = a n = a n × 1 : Thus a 0 = 1.

 
All Right Reserved. Copyright 2005-2024