# math (extra credit)!

posted by .

my teacher asked me why a number to the zero power is equal to 1. could you please explain why a number to the zero power equals 1?

• math (extra credit)! -

Consider first positive powers. Let's define:

f(a,n) = a^n

where a is a real number and n is a positive integer. This is well defined:

f(a,n) = a^n =
a*a*a...(n-factors in total).

Now, we haven't defined f(a,n) when n is not a positive integer, so, in theory, you are free to extend the function f(a,n) in any arbitrary way to other numbers. However, the function
f(a,n) has some nice properties and you want to preserve those when you extend the definition of f(a,n).

E.g.:

f(a,n+m) = f(a,n)*f(a,m)

If we want to extend the function to
n = 0 while not violating this equation, then we must choose f(a,0)= 1. To see this, take m = 0, in the above equation:

f(a,n) = f(a,n)*f(a,0) --->

f(a,0) = 1.

So, what mathematicians have done here (and in many other cases) is to take some of the properties of the function they want to extend to a larger set as the definition of the function (they uniquely define the function).

• math (extra credit)! -

thx but this didn't help i need to know why n^0= 1

• math (extra credit)! -

He told you, and I think it was the coolest answer yet!

## Respond to this Question

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The text passage contains a mathematical question and an explanation for the answer. The question is about why any non-zero number raised to the power of zero equals one. The explanation provided uses the properties of exponents to show that for the equation \(a^{n+m} = a^n \cdot a^m\) to hold true when \(m = 0\), it must be that \(a^0 = 1\).
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# math (extra credit)!

posted by .

my teacher asked me why a number to the zero power is equal to 1. could you please explain why a number to the zero power equals 1?

• math (extra credit)! -

Consider first positive powers. Let's define:

f(a,n) = a^n

where a is a real number and n is a positive integer. This is well defined:

f(a,n) = a^n =
a*a*a...(n-factors in total).

Now, we haven't defined f(a,n) when n is not a positive integer, so, in theory, you are free to extend the function f(a,n) in any arbitrary way to other numbers. However, the function
f(a,n) has some nice properties and you want to preserve those when you extend the definition of f(a,n).

E.g.:

f(a,n+m) = f(a,n)*f(a,m)

If we want to extend the function to
n = 0 while not violating this equation, then we must choose f(a,0)= 1. To see this, take m = 0, in the above equation:

f(a,n) = f(a,n)*f(a,0) --->

f(a,0) = 1.

So, what mathematicians have done here (and in many other cases) is to take some of the properties of the function they want to extend to a larger set as the definition of the function (they uniquely define the function).

• math (extra credit)! -

thx but this didn't help i need to know why n^0= 1

• math (extra credit)! -

He told you, and I think it was the coolest answer yet!

## Respond to this Question

 First Name School Subject Your Answer

## Similar Questions

1. ### math derivative please help

the derivative of 2x^e is zero right or no?
2. ### dividing monomials

i don't know what to do when their is a smaller number on top Give an example and tell us what you don't understand. (-c)2d7/c2d6 d i just don't get it do u have some examples?
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Is -4 to the zero power still 1 since all numbers to the zero power are 1 or is it negative 1?
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Selina has a homework consisting of 4 questions.In each question,she needs to find the value of each power.When she turns in her homework,her teacher says she got 3 correct answers which of the following values did she calculate incorrectly?

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user
The text passage contains a mathematical question and an explanation for the answer. The question is about why any non-zero number raised to the power of zero equals one. The explanation provided uses the properties of exponents to show that for the equation \(a^{n+m} = a^n \cdot a^m\) to hold true when \(m = 0\), it must be that \(a^0 = 1\).

TYPE: SINGLE_QUESTION_WITH_ANSWER