Question 250629
your equation the way you wrote it looks like this:


{{{((-3a^(-2) b^(-3) c^0 )^(-2))/((-2a^4 b^2 c^(-2) )^3 )}}}


That doesn't look right.


I think you may have wanted it to look like this:


{{{((-3a^(-2)*b^(-3)*c^0 )^(-2))/((-2a^4*b^2*c^(-2))^3 )}}}


I will assume my interpretation is correct and will solve for that.


Sinplify numerator and denominator by removing the outermost parentheses.


since {{{(x^a*y^b)^c = x^(a*c)*y^(b*c)}}}, your equation becomes:


{{{(-3^(-2)*a^(4)*b^(6)*c^0)/(-2^(3)*a^(12)*b^6*c^(-6))}}}


{{{a^4/a^12}}} = {{{a^(4-12)}}} = {{{a^(-8)}}} = {{{1/a^8}}}


{{{b^6/b^6}}} = {{{1/1}}}


{{{c^0/c^(-6)}}} = {{{c^0-(-6)}}} = {{{c^6}}}


your equation becomes:


{{{(-3^(-2)*c^6)/(-2^(3)*a^(8))}}}


{{{-3^(-2)}}} = {{{1/(-3^2)}}} = {{{(1/9)}}}


{{{-2^3}}} = {{{-8}}}


your equation becomes:


{{{((1/9)*c^6)/((-8)*a^(8))}}}


multiply numerator and denominator of this equation by 9 and you get:



{{{c^6/((-72)*a^(8))}}}


to confirm this answer is correct, we need to substitute some values in both the original equation and the final equation to see that they come out with the same answer.


we'll use:


a = 3
b = 4
c = 5


the original equation is:


{{{((-3a^(-2)*b^(-3)*c^0 )^(-2))/((-2a^4*b^2*c^(-2))^3 )}}}


after substitution, this becomes:


{{{((-3*(3)^(-2)*4^(-3)*5^0 )^(-2))/((-2*(3)^4*4^2*5^(-2))^3 )}}}


perorming indicated operations, this becomes:


{{{((-3*(1/9)*(1/64))^(-2))/((-2*81*16*(1/25))^3 )}}}


simplifying, this becomes:


36864/-1114512556 = -.033076343


the final equation is:


{{{c^6/((-72)*a^(8))}}}


after substitution, this becomes:


{{{(5)^6/((-72)*(3)^(8))}}}


this becomes:


15625 / -472392 = -.033076343


since the answer from the original equation and the final equation are the same, the simplification looks good.


your original equation of 
{{{((-3a^(-2)*b^(-3)*c^0 )^(-2))/((-2a^4*b^2*c^(-2))^3 )}}} simplifies to {{{c^6/((-72)*a^(8))}}}