Talking About Exponents

Date: 06/11/2002 at 03:27:50
From: Dxssi
Subject: Cubing Numbers

Here's a question some friends and I are debating over, and we'd like 
an expert's opinion, if you would be so kind. :)

Question: When a number is cubed how many times is it multiplied by 
itself?  Would you say 2 or 3 and why?

Work thus far: I say 2, because if 2^3 = 2 * 2 * 2, then you've 
multiplied 2 by itself twice.  To put it a different way, what if we 
multiplied 2 * 4 * 4, and made the question, "How many times did we 
multiply by 4?"  The answer would be two.

However, others disagree with me, and say the correct answer is 3, 
because there are three 2's.

Your help would be much appreciated, thank you!

Date: 06/11/2002 at 09:02:43
From: Doctor Ian
Subject: Re: Cubing Numbers

Hi,

I've never liked the phrasing 'multiplied by itself', because 
then you have to make special exceptions for 

  x^0 = 1

  x^1 = x

I prefer to say that x^n is 1 multiplied by x, n times.  So I'd 
say that a number cubed is 1 multiplied by the number, 3 times. 

Does this help? 

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