Question 164695
Let's take each chunk step by step.
First part:
{{{((4^(-2)*x*y^(-3))/(x^(-3)*y))^(3)=((4^(-6)*x^(3)*y^(-9))/(x^(-9)*y^3))}}}
{{{((4^(-2)*x*y^(-3))/(x^(-3)*y))^(3)=(4^(-6)*x^(3-(-9))*y^(-9-3)))}}}
{{{((4^(-2)*x*y^(-3))/(x^(-3)*y))^(3)=(4^(-6)*x^(12)*y^(-12)))}}}
Second part:
{{{((8^(-1)*x^(-2)*y)/(x^(4)*y^(-1)))^(-2)= (8^(2)*x^(4)*y^(-2))/(x^(-8)*y^(2)) }}}
{{{((8^(-1)*x^(-2)*y)/(x^(4)*y^(-1)))^(-2)= (8^(2)*x^(4-(-8))*y^(-2-2))) }}}
{{{((8^(-1)*x^(-2)*y)/(x^(4)*y^(-1)))^(-2)= (8^(2)*x^(12)*y^(-4))) }}}
Now let's multiply the first part by the second part:
{{{(4^(-6)*x^(12)*y^(-12))*(8^(2)*x^(12)*y^(-4))=4^(-6)*8^(2)*x^(12+12)*y^(-12-4) }}}
{{{(4^(-6)*x^(12)*y^(-12))*(8^(2)*x^(12)*y^(-4))=4^(-6)*8^(2)*x^(24)*y^(-16) }}}
Let's look at the constant,
{{{4^(-6)*8^(2)=4^(-6)*(2*4)^(2)}}}
{{{4^(-6)*8^(2)=4^(-6)*2^(2)*4^(2)}}}
{{{4^(-6)*8^(2)=4^(-6)*4*4^(2)}}}
{{{4^(-6)*8^(2)=4^((-6+1+2))}}}
{{{4^(-6)*8^(2)=4^((-3))}}}
{{{4^(-6)*8^(2)=1/64}}}
There's the 64.
{{{(4^(-6)*x^(12)*y^(-12))*(8^(2)*x^(12)*y^(-4))=(x^(24)*y^(-16))/64 }}}