A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 5 years ago
explain why any number (except 0) to the zero power always equals 1
anonymous
 5 years ago
explain why any number (except 0) to the zero power always equals 1

This Question is Closed

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[a^0=a^{bb}=a^b\cdot a^{b}=a^b\cdot\frac{1}{a^b}=1\]

nowhereman
 5 years ago
Best ResponseYou've already chosen the best response.0Because 1 is the neutral element of the multiplicative group of real numbers except 0.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0please use smaller words "nowhereman" i am going to write this on thetest and i cant sound overlly smart

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0nikvist's algebraic interpretation is correct.

nowhereman
 5 years ago
Best ResponseYou've already chosen the best response.0The above calculation is quite good already. You could also write: \[a^0 \cdot a^n = a^{0+n} = a^n\] so \[a^0 = 1\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0explain why 0 to the 0 power is not one

nowhereman
 5 years ago
Best ResponseYou've already chosen the best response.0Because it is undefined. For the exponential function 0^x to be continuous it must be 1 but for x^0 to be continuous it must be 0. So you can't define it consistently (e.g. so that all powerrules hold)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Or you can go back to nikvist's explanation and realize that to get \[0^0\] you'd have to divide by 0 which isn't defined.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0"The choice whether to define 0^0 is based on convenience, not on correctness"

nowhereman
 5 years ago
Best ResponseYou've already chosen the best response.0Well, what is correctness anyway. After all you choose which axioms you rely on.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Don't shoot the messenger :(

nowhereman
 5 years ago
Best ResponseYou've already chosen the best response.0Whos quote was it then?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Donald C. Benson, The Moment of Proof : Mathematical Epiphanies. New York Oxford University Press (UK), 1999.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.