Shortcut for Computing x^n

Date: 07/05/2002 at 09:59:53
From: Imran
Subject: How to solve x^n as fast as possible

Dear Dr. Math,

Our teacher asked us to solve 3^12.  We did 3*3*3*3..... and got the
answer 531441.

In the course of the rest time, my classmate asked me how to solve x^n
as fast as possible.  I have no idea. 

Do you have any formula or shortcut?

Thank you very much for your time,
Imran.

Date: 07/16/2002 at 09:14:20
From: Doctor Nitrogen
Subject: Re: How to solve x^n as fast as possible

Imran:

Why not just use the associative law to make it easier? 

That is:

    3^12 = (3*3*3*3)*(3*3*3*3)*(3*3*3*3) = (3^4)*(3^4)*(3^4)

         = (81)*(81)*(81) = 81^3 = 531441.

This can be done no matter what number x in x^n stands for and 
for any positive integer n > 3.  

Hope this helps. 

- Doctor Nitrogen, The Math Forum
  http://mathforum.org/dr.math/