Answer: [tex]\frac{4x^{14}}{y^{8}}[/tex]
Step-by-step explanation:
We have tthe following expression:
[tex](\frac{2^{-3} }{x^{-3}} \frac{y^{2}}{4^{-2}} \frac{x^{4}}{y^{6}})^{2}[/tex]
Firstly, we have to solve the oeprations inside the parenthesis. Let's begin by grouping similar coefficients:
[tex](\frac{2^{-3} }{4^{-2}} \frac{x^{4}}{x^{-3}} \frac{y^{2}}{y^{6}})^{2}[/tex]
Rewriting the expression:
[tex](\frac{4^{2} }{2^{3}} x^{4} x^{3}\frac{1}{y^{4}})^{2}[/tex]
[tex](\frac{2x^{7} }{y^{4}})^{2}[/tex]
Multiplying the exponent outside the parenthesis with the exponents inside:
[tex]\frac{4x^{14}}{y^{8}}[/tex] This is the final result
