Answer: [tex]\frac{4}{x^{14} y^{8}}[/tex]
Step-by-step explanation:
We have the following expression:
[tex](\frac{2^{-3} x^{-3} y^{2}}{4^{-2} x^{4} y^{6}})^{2}[/tex]
First, we have to solve what is inside the parenthesis, taking into account the addition and substraction of exponents with the same base:
[tex](\frac{4^{2} y^{2}}{2^{3}x^{4} x^{3} y^{6}})^{2}[/tex]
[tex](\frac{16}{8 x^{7} y^{4} })^{2}=(\frac{2}{x^{7} y^{4} })^{2}[/tex]
Finally:
[tex]\frac{4}{x^{14} y^{8}}[/tex]
