Why does the rule say that,if a^x=a^y,when a is greater than 0 and a is not equal to 1?what if a were less than 0?

Question

I am an 6th grade student.And just learning the rules of exponents . Please don't close the question.An explanation would be appreciable and I'll be very great full if the question is answered.

Answer 1

If $a<0,$ then the expression $$a^x$$ doesn't always have a definite real value for an arbitrary real number $x.$ But we often want something like this -- and we always have at least one real value for $a^x$ whenever $a>0.$ We usually choose the positive of these as the meaning of $a^x,$ when there are more than one possibility. We rule out the case $a=1$ since then we would always have the same value for $a^x$ regardless what value $x$ assumes.