Introduction to Powers and Roots

Raising a number to a power P means multiplying the number by itself P times.

It is usually denoted with the symbol ^ or **.

 

For example,

        3^0 = 1

        3^1 = 3 = 3

        3^2 = 3*3 = 9

        3^3 = 3 * 3 * 3 = 27

        3^4 = 3 * 3 * 3 * 3 = 81

 

Raising any number to 0 is always defined as 1.

When you use ^2 it is called squaring, and ^3 is calling cubing.

 

 

The opposite function is called finding the root.  It means taking a number n and a root r, and returning the number that, if raised to power r, will give n.  The symbol is hard to show on the computer, so, for a moment, we will just call it rootr().

 

For example,

         root1(3) = 3

         root2(9) = 3

         root3(27) = 3

         root4(81) = 3

 

Now, just like subtraction is adding a negative number, and dividing is multiplying a fraction, roots can be expressed as raising to a fractional power.

 

So,

       3^(1/1) = 3  because 3^1 = 3

       9^(1/2) = 3    because 3^2 = 9

       27^(1/3) = 3  because 3^3 = 27

       81^(1/4) = 3  because 3^4 = 81