how do you find something raised to the -1 power?

Question

anonymous · Answer

You take the mulitplicative inverse of the expression. For example: 
a^-1 = 1/a

anonymous · Answer

ok so 2 raised to -1 is 1/2?

anonymous · Answer

Yes.

anonymous · Answer

thanks i compeltely forgot

anonymous · Answer

And 2 raised to -2 is 1/4.

anonymous · Answer

that i remember but i just forgot -1

anonymous · Answer

wait but when does something raised to something power equal 1?

anonymous · Answer

raised to the 0 power.

anonymous · Answer

thanks it's all coming back to me now

anonymous · Answer

Negative exponents are inverses (x^-1 = 1/x).  Fractional exponents are roots (x^(1/2) is sqrt(x)).  0 exponents are 1 (x^0 = 1).

anonymous · Answer

And we would go on with the rules: 
(a)^b*(a^c) = a^(b+c)
(a^b)^c = a^(bc)

Important rules, even though they seem very innocent.

phi · Answer

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agreene · Answer

Phi, you can also use what most post WWII number theorists use...
We define exponents in the following logarithmic method:
$$\large n^x=e^{x \ln (n)}$$
putting in 0 for x:
$$n^0 = e^{0 \ln(n)}$$
$$n^0 = e^{0}$$
$$\therefore n^0=1\space |\space  \forall : n \ne 0 $$

phi · Answer

That will mean anything to a kid in high school?

agreene · Answer

Well, in order to understand recursion... one must first understand recursion... in order to understand recursion...

It's a rather straightforward collapsing proof... so I'd like to think they'd get it.

agreene · Answer

And maybe it will help them remember the rules of exponents, cause in that general logarithmic form... it self defines every exponential form, which is fancy.