pre algerbra

Any particular reason why you are posting this again?
 
tkhunny said:
Any particular reason why you are posting this again?
Click to expand...
well my book says any thing with a zero power =1 .........- (-3)^0=-1 ??? i dont get it why 0 or why -1





9
 
I suppose there are various explanations, but you may just want to commit this one to memory as a definition.

\(\displaystyle a^{0}\;=\;1\) for \(\displaystyle a \in \mathbb{R}\) and \(\displaystyle a \ne 0\).
 
earlbrewer said:
well im confused my book says any thing with a zero power = 1
Click to expand...
The SHORT answer is that a[sup:lk06zz2f]0[/sup:lk06zz2f] is DEFINED to equal 1. Why is a table called a "table" and not a "biff"? Because we have agreed to call it a table BY DEFINITION. Similarly with a[sup:lk06zz2f]0[/sup:lk06zz2f], we have agreed to call it 1 BY DEFINITION.

The LONG answer explains why that definition is useful.

The fundamental idea behind powers STARTED with the idea of multiple multiplication.
a[sup:lk06zz2f]1[/sup:lk06zz2f] = a
a[sup:lk06zz2f]2[/sup:lk06zz2f] = a * a
a[sup:lk06zz2f]3[/sup:lk06zz2f] = a * a * a

Notice that the zero and negative powers make no sense with that definition of a power.

You can, however, derive a law of exponents from that definition, namely a[sup:lk06zz2f]b[/sup:lk06zz2f] * a[sup:lk06zz2f]c[/sup:lk06zz2f] = a[sup:lk06zz2f]b+c[/sup:lk06zz2f].

That leads to the idea of DEFINING a[sup:lk06zz2f]-1[/sup:lk06zz2f] = 1/a because
(1/a)* a[sup:lk06zz2f]2[/sup:lk06zz2f] = (a * a) / a = a = a[sup:lk06zz2f]1[/sup:lk06zz2f] = a[sup:lk06zz2f]2-1[/sup:lk06zz2f]
(1/a) * a[sup:lk06zz2f]3[/sup:lk06zz2f] = (a * a * a) / a = a * a = a[sup:lk06zz2f]2[/sup:lk06zz2f] = a[sup:lk06zz2f]3-1[/sup:lk06zz2f]
(1/a) * a[sup:lk06zz2f]4[/sup:lk06zz2f] = (a * a * a * a) = a * a * a = a[sup:lk06zz2f]3[/sup:lk06zz2f] = a[sup:lk06zz2f]4-1[/sup:lk06zz2f]

So now there is a definition of powers that includes multiplication and its inverse of division and positive and negative powers, and in addition, EXCEPT FOR ONE CASE, maintains the law of exponents.

The case where the law of exponents raises a question is this one: a[sup:lk06zz2f]b[/sup:lk06zz2f] * a[sup:lk06zz2f]-b[/sup:lk06zz2f] = a[sup:lk06zz2f]b-b[/sup:lk06zz2f] = a[sup:lk06zz2f]0[/sup:lk06zz2f], but a[sup:lk06zz2f]0[/sup:lk06zz2f] has not YET been defined.
However, a[sup:lk06zz2f]b[/sup:lk06zz2f] * a[sup:lk06zz2f]-b[/sup:lk06zz2f] = a[sup:lk06zz2f]b[/sup:lk06zz2f] * (1/a[sup:lk06zz2f]b[/sup:lk06zz2f]) = a[sup:lk06zz2f]b[/sup:lk06zz2f] / a[sup:lk06zz2f]b[/sup:lk06zz2f] = 1.
So, in order to maintain the law of exponents, we DEFINE a[sup:lk06zz2f]0[/sup:lk06zz2f] = 1.

Make sense now?

PS 0 to a negative power is undefined so the case of 0[sup:lk06zz2f]a[/sup:lk06zz2f] * 0[sup:lk06zz2f]-a[/sup:lk06zz2f] cannot arise. So some people say 0[sup:lk06zz2f]0[/sup:lk06zz2f] is undefined. Others define 0[sup:lk06zz2f]0[/sup:lk06zz2f] = 1. Do whatever your teacher tells you to do about that one.
 


earlbrewer said:
well im confused my book says any thing with a zero power = 1
Click to expand...

Your confusion is not a good-enough reason to start a second thread on this same topic.

If you post a question on these boards, and you do not understand a response that you get, then continue posting your additional questions in the same thread.

Do not start a new thread each time you want to say something because your conversation will end up spread all over the place on the boards.

For example, I just responded to your original thread, not knowing that you repeated your question in this thread. (Kindly click HERE to go there.)

Splitting your conversation up into bits and pieces is a waste of volunteers' time. I hope that you understand this now.

We only start new threads when we want to talk about a different exercise or new topic.

Cheers 8-)

 
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