Easier Way to Evaluate Powers

Date: 9/7/96 at 0:30:59
From: Randy Dority
Subject: Easier Way to Evaluate Powers

Do you know of any shortcuts to finding the answer to powers?
Example:  7 to the 9th power = x

Jonathan

Date: 9/12/96 at 10:23:51
From: Doctor Jerry
Subject: Re: Easier Way to Evaluate Powers

While I'll mention one idea below, there are no real shortcuts to 
finding powers of numbers (without just doing it on a calculator).  
This is one reason that the invention of logarithms 400 years ago was 
thought to be such a time-saving invention. It saved many, many people 
a lot of time.

I'll use the carat (^) notation for powers: 7 to the 9th power is 
7^9.

The calculation can be divided in various ways.  For example,

7^9 = (7^3)^3 

So, if you know or calculate 7^3 = 343, then
7^9 = 343*343*343 = 40,353,607.

Or, 7^9 = (((7^2)^2)^2)*7 = ((49^2)^2)*7 = (2401^2)*7 = 5,764,801*7 = 
40,353,607.

I like the first way better.  It seems easier.

Here's another problem:

2^10 = (2^5)^2 = 32^2 = 1024.

How would you do 8^5?

-Doctor Jerry,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/