Laws of Indices

 

 

How do we perform the 4 basic operations on indices? Indices generally follow the following laws:

 

         Laws of Indices: 

                             a^m x aⁿ = a^m+n

                             a^m / aⁿ = a^m-n

                            (a^m)ⁿ = a^mn

                             a^m . b^m = (ab)^m

                           

 

To prove this, we can substitute numbers into the identities. Take 2³ X 2⁵. Using a calculator, you will get 256. Using the law, you will get 2³⁺⁵ = 2⁸ =256. The other laws can be proven similarly. Also refer to our article on history of algebra, algebra of polynomials.

 

       Other useful properties of indices: 

                       a⁰= 1

                                 

                                  

 

 

Simplify the following expressions:

 

x^-2. x³

 

  Solution:

                 x^-2. x³

                               =  x^-2+3   

                       = x^-1

 

 

  Solution:

                    =

                                  = x^-0.5

 

 

  Solution:

            

                                 =

                                 =

                                 =