Question 278925
<pre><font size = 4 color = "indigo"><b>

You and the other tutor both missed the sign.  The answer
is positive not negative!  
Never confuse {{{-4^(exponent)}}} with {{{(-4)^(exponent)}}}!  That is
a very common error!

{{{(-4^(-6)y^(-6))^(-4)}}}

Consider the negative sign in front to be {{{(-1)^1*""}}}

{{{((-1)^1*4^(-6)y^(-6))^(-4)}}}

Next remove the parentheses by multiplying each 
of the three inside exponents by the outside exponent {{{-4}}}


{{{(-1)^(-4)*4^(""+24)y^(""+24)}}}

The term in front is {{{""+1}}} because of the rule

{{{negative^(even)=positive}}},  {{{negative^(odd)=negative}}}

So the final answer is

{{{4^24y^24}}}

Edwin</pre>