[Guest]

Ok everyone!

Without picking at wikipedia or anywhere else, can you prove that any number under the power of zero equals to 1?

x⁰ = 1

Edited November 16, 2010 by Tsopi

[k-man]

x⁰ = x^n-n = xⁿ / xⁿ = 1

[Guest]

this assumes we've established that x ^ (y-z) = x^y/x^z

let y=z, then

x^(y-z) = x^(y-y) = x^0

x^(y-z) = x^y/x^z = x^y/x^y = 1

therefore x^0 =1

sloppy but...

[Guest]

aww man, k-man beat me...you're lucky you're on the EDT

[Guest]

My understanding is that the x⁰ = 1 by definition. One often sees proofs based on the law of exponents (as above), but I haven't seen a proof of the law of exponents that didn't implicitly assume that a x⁰ = 1.

[Akriti]

x^a-a=x^a/x^a=1

Hence proved.

[Guest]

Ok everyone!

Without picking at wikipedia or anywhere else, can you prove that any number under the power of zero equals to 1?

x⁰ = 1

x^(a-a) = x^a / x^a = 1

[k-man]

aww man, k-man beat me...you're lucky you're on the EDT

How does it help me being on EDT?

[Guest]

the joke was funnier in my head...basically it was 8:51 am for you before it was for me (or for you it was 9:51 am for you before it was for me)

[Guest]

I prove this to my middle schoolers through a simple explanation using the chart below

3^1 3^2 3^3 3^4 3^5

3 9 27 81 243

As we go to the right, the values are multiplied by 3, and the exponents go up by one. Following a similar pattern, as we go to the left, the values are divided by 3, and the exponents go down by one. When you get to 3^1, and you continue the chart, you get 3/3 is 1, and the exponent goes down one to zero.

This can be continued to show how negative exponents give smaller numbers and place values as well.

[Guest]

Heyyyy its still not solved yet guys, for unfortunately , your answer z not general because u stated

X⁰=X^n-n=Xⁿ/Xⁿ=1 (((( but the question still why 0⁰=1

and the prev sloving is not workin for this case because we cannot divide by X⁰=0 )))

so let's think why this case is also 0^0=1 ^^))

Edited November 18, 2010 by dibasoufiane

[Guest]

nm

Edited November 18, 2010 by maurice