Answer:
![(4x^(14))/(y^(8))](https://img.qammunity.org/2021/formulas/mathematics/middle-school/k8ti9eu0bph5a1oc4vgfh1jjqdoxbjgnhd.png)
Explanation:
We have tthe following expression:
![((2^(-3) )/(x^(-3)) (y^(2))/(4^(-2)) (x^(4))/(y^(6)))^(2)](https://img.qammunity.org/2021/formulas/mathematics/middle-school/gw76yhuolnx0qiq78zzc5ku6fqnnlkdsw6.png)
Firstly, we have to solve the oeprations inside the parenthesis. Let's begin by grouping similar coefficients:
![((2^(-3) )/(4^(-2)) (x^(4))/(x^(-3)) (y^(2))/(y^(6)))^(2)](https://img.qammunity.org/2021/formulas/mathematics/middle-school/p8sc6l9miwkix4v94mrd5ccjtbrxpspdcd.png)
Rewriting the expression:
![((4^(2) )/(2^(3)) x^(4) x^(3)(1)/(y^(4)))^(2)](https://img.qammunity.org/2021/formulas/mathematics/middle-school/12ovdkqr5chze11ixn56kg23f47dlpktdd.png)
![((2x^(7) )/(y^(4)))^(2)](https://img.qammunity.org/2021/formulas/mathematics/middle-school/n5tmtjr0jwt9463z91y34afou4jc23jz61.png)
Multiplying the exponent outside the parenthesis with the exponents inside:
This is the final result