Why 2 power 0 equals 1?

Answer 1

Here is why any number to the zero power equals one.

Consider this.

a^b. it is natural to restrict a > 0, but we'll only assume that number b is any real number.

We'll use the natural exponential function defined by the derivative of the exponential function.

Now we have a^r=e^rln(a). And we know that e^rln(a)=e^((ln(a))^r), where a >0 and r is in the domain of all real numbers negative infinity to infinity.

We can apply this definition to any number a to any power r.

Particularly, a^0. By the provided definition, a^0=e^(0*ln(a))=e^0=1.

Furthermore, a^1=e^(1*ln(a))=e(ln(a))=a.

And a^2=(e^(ln(a))^2)=a^2.