a hard one i think..?

Question

who can proove that 0 to the power of 0?

i mean it is not equal to 1

oooppsss sorry i asked a wrong questioni know this one, sorry... my question was who can proove that 100 to the power of 0 is equal to one.

coz someone told me that there is a really long solution for it

Answer 1

100^0 = 1...

You could do it though limits, here is an intuitive approach that might explain it.

100^2 is 100 squared, so 10000
100^1 is 100, plain as it is
100^0.5 is the square root of 100, hence 10.

This last one can intuitively be understood as

100^0.5 = 10
100 = 10 ^(1/0.5)

Basically, 100^0.5 can be taken as meaning "what is the number that is raised to the power of 1/0.5 that will return 100?

Got that? Ok, moving on.

100^0.1 therefore means what number is raised to the power of 10 (1/0.1) yielding 100?

Now, we can decrease the exponent as far as we want, nealry to zero, so in the end we have the question "what is the number that is raised to infinity that would yield 100?

Only one can be multiplied by itself an infinite number of time and possibly have a glimmer of hope of getting a finite answer. Any number larger than 1 will quickly grow to infinity, and numbers smaller than 1 (but still positive) will reduce to zero.

Answer 2

The statement to prove:
100^0 = 1

1) Using the reflexive property
100^0 = 100^0

2) Using the reflexive property,
1 = 1

3) Using Addition property of equality, add -1 to both sides,
1 - 1 = 0

4) Using the symmetric property
0 = 1 - 1

5) Using the substitution principle, in statement 1, substitute the value of 0 as 1 - 1:
100^0 = 100^(1 - 1)

6) Using one of the properties of exponents b^(x + y) = b^x b^y,
100^0 = 100^(1 - 1) = 100^1 · 100^(-1)

7) Using substitution principle, since 100^1 = 100, and 100^(-1) = 1/100,
100^0 = 100^1 · 100^(-1) = 100 · 1/100

8) Using the multiplicative identity property, since 1/100 is the multiplicative inverse of 100, their product is 1
100^0 = 100 · 1/100 = 1

9) Therefore, using the transitive property of equality,
100^0 = 1
QED

^_^

Answer 3

100^0 = X solve for X

1) take the log of both sides:
log (100^0) = log(X)

2) since log(Y^Z) = Z x log(Y)
0 x log(100) = log(X)

3) since log(100)=2
0 x 2 = log(X)

4) since 0 x 2 = 0
0 = log(X)

5) swap
log(X) = 0

6) the only value of X that satisfies the equation is 1, therefore
X = 1

finally:
X^0 = 1 for all X except 0
why?:
0^0 is undefined because line 2 (above) would be 0 x log(0).
since log(0) is infinity, 0 x infinity is undefined (by definition)
therefore, 0^0 is undefined

Answer 4

0, zero times cannot equal anything
0 x 0=0 0 x 0=0

Answer 5

You know how you subtract exponents when you divide? Well take 100^2/100^2. Subtract exponents and that's 100^0 but we all know any number divided b y itself is one so 100^0 = 1

Answer 6

Let x=y, let z=-4, and b=banana. sub.0 for F and divide by 0. Therefore any F n thing becomes 0

Answer 7

Anything raised to the 0 power is one. Zero might be the lone exception.

Answer 8

1^0=0, 0 times (x) any number including another Zero is Zero, Any number divided by 0, is zero...

--For more information, click on the link below--

Answer 9

0 is nothing. So, nothing to the power of nothing: nothing happens.

Answer 10

can't u just use a calculator and see if it's true? well sorry i don't think i can ^-^ and btw cardcaptor sakura is really kool~ heh heh i used to watch it all the time!