Power of 120

Date: 06/12/2001 at 11:43:09
From: Grabowski
Subject: Exponents

Is there a quick way to work out 1.05 to the power of 120?  The only 
way I can think of is to take 1.05 and keep multiplying it by itself, 
120 times.

Date: 06/12/2001 at 12:31:37
From: Doctor Peterson
Subject: Re: Exponents

Hi, Grabowski -

I would use a scientific calculator, which has an exponent key. (My 
computer has one in the Accessories menu.)

If I had to do it by hand, I would save some work by repeatedly 
squaring, rather than just multiplying by 1.05 itself. You can then 
multiply some of these powers together to get what you want.

As an example, 1.05^5 is 1.05^4 * 1.05^1, so you can calculate it by 
squaring until you get 1.05^4

    1.05^1 = 1.05
    1.05^2 = 1.1025
    1.05^4 = 1.2155

and then multiplying 1.2155*1.05=1.276. This took only three 
multiplications rather than 4; for larger exponents the savings will 
be much greater.

In your case, I would square 6 times until I got 1.05^64, and then 
multiply four of these numbers together, so it takes only 9 
multiplications.

If you've learned about the binary number system at all, you'll find 
that to be helpful.

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