Question

There is no war in Ba Sing Se.

Answer 1

\[x^0 = 1 \]
\[0^0 = 1? \]

Answer 2

Because, well, 0 . . .

Answer 3

0^0 = 1

Answer 4

No, 0^0 is undefined

Answer 5

0^0=0^1/0^1=0/0=infinity

Answer 6

thesmartone you are not smart xD

Answer 7

you cannot divide by 0

Answer 8

Google doesn't lie
https://www.google.com/q=0%5E%200%20%3D

Answer 9

You can't deal with intermediate forms algebraically

Answer 10

\[0^0=\frac{ 0^1 }{ 0^1 }=\frac{ 0 }{ 0 }=\infty \]

Answer 11

err as in pre calculus uh what

Answer 12

0 is the exception for this rule

Answer 13

So 7^7 is the same as 7/7?

I didn't know that.

Answer 14

no

Answer 15

7^7=7*7*7*7*7*7*7*7 not 7/7

Answer 16

They always just say if the exponent is 0, it equals 1 but they never really gave an explanation with it so I couldn't tell what 0^0 was

Answer 17

because x cannot be 0

Answer 18

7^7=7^14/7^7

Answer 19

I meant 7^0 not 7^7 woops

Answer 20

yes

Answer 21

WOOpS

Answer 22

because 7^0=7^1/7^1-7/7=1

Answer 23

woops i meant =

Answer 24

not -

Answer 25

http://mathforum.org/dr.math/faq/faq.0.to.0.power.html

Answer 26

First of all, great question.
\[0^0\]
This is what's called an indeterminate form. We can't say anything about what this means unless it shows up in a specific context! There are times when \(0^0=1\) and there are other times where \(0^0=0\) and it can be other things as well!

How do we determine what its true value is then? That's what calculus allows us to answer.

Answer 27

It is uncertain , and mathematics is about certainities , so it is mathematically undefined

Answer 28

Like the same way you cannot divide by 0 :)

Answer 29

One way to side step the problem is to define exponents to tell you how many times you multiply the number by 1. For instance:
\[a^b\]

This means multiply \(a\) by \(1\) for \(b\) times.

An example of this is:
\[2^3 = 1*2*2*2\]\[2^1 = 1*2\]\[2^0=1\]

\[0^3 = 1*0*0*0\]\[0^1 = 1*0\]\[0^0 = 1\]

Answer 30

this is a mystery

Answer 31

using what kainui said 0^0=1

using the main method 0^0=infinity

Answer 32

0^0 is same as 0/0

Answer 33

That's a pretty clear way to explain it, makes a lot of sense now. Ofc this will always be a weird question and probably has a lot of answers, but that's one clear way.

But yeah, I guess it does depend on context.