Why is -2 raised to 0 = 1, a debt powered by nothing is equals to something (1) , why???

Question

explain using your own words. d not repeat rule that i can read from book. make an example in real life if possible.. i cannot imagine it

Answer 1

Think of it in the following way:
(-2^1) / (-2^1) = 1 because the numerator and denominator are the same.

(-2^1) / (-2^1) = -2^0
because you can just subtract exponents when dividing these
therefore -2^0 = 1

Answer 2

One way to think of it is that n^k = 1*n*n*...*n (k n's). 1 is the multiplicative identity. The 1 is always there, and n^k is multiplying the 1 by k n's, and if k=0, then you're multiplying 1 times no n's, which is just 1.

Don't think of it as a debt. To think of it as a debt requires you to use addition not multiplication; after all when 3 people owe you $10, the total debt owed to you is $30, not ($10)^3=($^3)*1000. There is an analogy: multiplication is to powers as addition is to multiplication; e.g., 4*4*4*4*4 = 4^5 while 4+4+4+4+4 = 4*5. Then it makes sense to say that a debt multiplied by 0 is no debt because your adding nothing to 0 (0 is the additive identity, and so it is always a summand of a sum, just as 1 is always a factor of a product as was mentioned in the first part above)

Answer 3

Mathematical terms are defined precisely and usually somewhat differently than they are commonly used. "-" means the additive inverse of, or what number when added to the given number means 0. It does not necessarily mean a debt. Power means multiply that many times; 2 to the 4th power is 2x2x2x2 = 16. It does not mean electricity or ability to get others to do something for you.

You remind me of a slogan I have heard a while ago, one for motivating people to succeed. A former International Director of Toastmasters used it when she was a District Governor: The Power of One. What she did not realize was that 1 raised to any power is 1. Maybe she should have tried "The Power of Two".

Answer 4

It's needed for math to work really. If it weren't true, math wouldn't be math. 2^3 = 8, 2^2=4 2^1 =2 2^0 =1 2^-1 so 8,4,2,1,1/2

It's a geometric progression that's a consequence of number theory.

Answer 5

I`ll start from the concept of powering , when a number is powered for example in two that means it has been multiplied in itself two times like 2^3= 2.2.2
so , when a number is powered to nothing (0) that means it hasn`t been multiplied in itself and that means it`s 1 ! Got it?

Answer 6

Take this demostration:

H^0 = H^(a-a) ; a-a = 0 then

= H^a*H^-a = >

= H^a * (1/H^a)

= H^a/H^a = 1

THAT IS WHY

H^0 = 1

I wish that I could put this in words, but I don't speak English.

Espero te haya ayudado