Domain of definition of the function f(x,y)=x^y

[Amaelle]

Homework Statement

find the domain of definition of the function f(x,y)=x^y

Relevant Equations

the domain of definition of the function

Good day
as said in the title i need the domain of definition of of the function f(x,y)=x^y
for me as x^y=expontial (y*ln(x)) so x>0

but the solution said more than that

I really don't understand why we consider the case (0,y) in which while should be different from 0, because I will never have an x=0?

many thanks in advance

 

[BvU]

Apparently the function is defined for $x=0, \ y\ne 0$ :

because zero to any power (other than the zero power) is zero

for me as x^y=expontial (y*ln(x)) so x>0

It is the other way around: IF $x>0$ THEN $\ln(x)$ exists AND ...

 

[Amaelle]

thanks a lot!