Question 21897
First of all, in the equation {{{3^4=(-3)^4}}}, there is no "hidden" 1.  
Well, there could be in the second part {{{1(-3)^4}}}, but it still would not affect the answer because it's outside of the parenthesis. 
So, in fact, {{{3^4=(-3)^4}}} is TRUE.  


You probably know that two negatives make a positive number.
So, {{{-3*-3*-3*-3}}} will be equal to {{{3*3*3*3}}}, which is 81


HOWEVER, if the negative sign was on the outside of the parenthesis, it would make the 2 equations different.  For example, {{{-(3*3*3*3)}}} would be different from {{{3*3*3*3}}} because the negative is on the outside, which makes the whole product negative.  That's where the "hidden" 1 comes in.  In {{{-(3*3*3*3)}}}, it's not 1, it's -1.  


The Law of Exponents is (and there are many more):
{{{(ab)^c}}}={{{a^c*b^c}}}
So I don't know where you got {{{(xy)^4=xy}}} because that is completly wrong.  
Hope this helps!