Jump to content

Menu

Algebra 2 problem: a to the zero


Recommended Posts

0 to the 0 power is undefined' date=' but if it could be defined, it would be 1.

 

Here's the explanation:

 

http://www.math.hmc.edu/funfacts/ffiles/10005.3-5.shtml[/quote']

 

I disagree with their assessment of the situation.

 

The essential reason why it is undefined is that the limit of x^y as (x,y)-> (0,0) may attain any value depending on the path chosen, hence the limit doesn't exist.

 

There are some circumstances (which they've listed, and done a good job of explaining) where it makes sense to "consider" it as one, but teaching either that it is one or should be one in a more general case will lead to difficulties both with indeterminate forms in l'Hospital's rule and with multivariate functions, where it certainly doesn't always equal 1.

 

In general, I believe that it should be avoided to teach something young (such as saying that x/0 = infinity) which will need to be untaught later.

Link to comment
Share on other sites

I understand a to the zero power is 1. What happens when a is a negative number? For instance, a to the zero when a is -3? Is the answer +3 or -3?

 

The key here is figuring out what is the base.

 

-3^0, the base is 3 which is raised to the 0, then the answer is negated, thus -3^0 = -1

 

(-3)^0, the base here is -3, raised to the 0, so the answer is 1

 

5x^0, the base is x, so we have 5(1) = 5.

(5x)^0, the base is 5x, so we have 1.

 

Some calculators will handle -3^0 correctly, others incorrectly, so it's good to experiment with your model if you're using the calculator.

Link to comment
Share on other sites

a^0 (a to the zero power) is the same thing as:

 

a/a

 

if you 'subtract' the exponent (hidden 1) from the numerator and the denominator you are left with 1/1. This works as long as a is a non-zero integer (so positive and negative non zero are ok).

 

Why does a have to be an integer? Doesn't this also work if a is any real number?

Link to comment
Share on other sites

Yes.

 

Thanks for the reply.

Are these the correct answers? (I don't get the trick!)

 

Say the opposite of these words: 1. Always 2. Coming 3. From 4. Take 5. Me 6. Down

 

 

1. never

2. going

3. to

4. give

5. you

6. up

 

I feel really stupid. :confused:

Link to comment
Share on other sites

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

Guest
Reply to this topic...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

 Share

×
×
  • Create New...