ANSWER
y³⁶/x⁸
EXPLANATION
To simplify this expression we have to do it from the inner part of the expression to the outer part. First, we have x⁰, which is equal to 1,
[tex](x^2y^3(x^0y^{-4})^3)^{-4}=(x^2y^3(y^{-4})^3)^{-4}[/tex]Then we have the interior parenthesis. To simplify this we have to apply the exponent of exponent rule,
[tex](a^b)^c=a^{b\cdot c}[/tex]So we have,
[tex](x^2y^3(y^{-4})^3)^{-4}=(x^2y^3y^{-4\cdot3})^{-4}=(x^2y^3y^{-12})^{-4}[/tex]Next, apply the product rule of exponents with the same base,
[tex]a^b\cdot a^c=a^{b+c}[/tex]In this case,
[tex](x^2(y^3y^{-12}))^{-4}=(x^2y^{3-12})^{-4}=(x^2y^{-9})^{-4}[/tex]The exponents can be distributed into the multiplication, so we have,
[tex](x^2y^{-9})^{-4}=(x^2)^{-4}(y^{-9})^{-4}[/tex]Apply the exponent of exponent rule again,
[tex](x^2)^{-4}(y^{-9})^{-4}=x^{2(-4)}y^{(-9)(-4)}=x^{-8}y^{36}[/tex]Finally, negative exponents flip the base,
[tex]a^{-b}=\frac{1}{a^b}[/tex]Hence, the simplified expression is,
[tex]\frac{y^{36}}{x^8}[/tex]