What does this rule mean?

Question

I read this rule in a book .it says, If $a>0$, $a$ is not equal to $1$ and $a^x=a^y$,then $x=y$. But I don't understand why the value of $a$ has to be greater than $0$. What if the value of $a$ was less than $0$? Wouldn't it be the same ?For example, if $a=-2$, for which other value of $x$,could I get $4$ other than $2$?

Answer 1

When $a<0$ exponentiation is not well defined for $x \in \mathbb R$.

Note that for $a>0$, $a\neq 1$ the equality $x=y$ from $a^x=a^y$ holds since $f(x)=a^x$ is injective.