Thread: Powers of 0 and 1

We all know that any number or variable raised to the zero power equals 1
and that any number or variable raised to the 1st power equals the number or variable.

SAMPLE A:

x^0 = 1 as well as 100^0 = 1

SAMPLE B:

x^1 = x as well as 100^1 = 100

Why is this the case?

Can anyone explain, in simple terms, the WHY concerning the above?

I'll do the why of

x^0 = 1

. We have . EDIT : Or even better, because (From the definition of the logarithm function. If you define the exponential function as the inverse function of the logarithm one, then what I wrote holds.). Note that it holds .

Originally Posted by magentarita

We all know that any number or variable raised to the zero power equals 1
and that any number or variable raised to the 1st power equals the number or variable.

SAMPLE A:

x^0 = 1 as well as 100^0 = 1

SAMPLE B:

x^1 = x as well as 100^1 = 100

Why is this the case?

Can anyone explain, in simple terms, the WHY concerning the above?

Assuming you buy Arbolis's post then



Or more obvious



Assuming

I thank you both for that great mathematical insight.