Answer:
[tex](a) \: \underline{\boxed{ ans = \frac{5}{3}}} \\ (b) \: \underline{ \boxed{ans = \frac{x}{y} }}[/tex]
Step-by-step explanation:
[tex]if \: the \: question \: is \to simplify \\ a).......... { ( \frac{3}{5})^{ - 2} ÷ (\frac{5}{3})^{2} } + \frac{5}{3} \\ \\ b)....( \frac{x}{y})^{ - 2} × ( \frac{x}{y})^{ 4} × ( \frac{x}{y})^{ - 1} \\ \\ \underline{ \boxed{solution....(a)}} \\ \\ (\frac{3}{5} )^{ - 2} \div \: (\frac{3}{5} )^{ 2} + \frac{5}{3} = \\ \\ \frac{1}{(\frac{3}{5})^{2}} \div \: (\frac{3}{5} )^{ 2} + \frac{5}{3} = \\ \\ (\frac{5}{3} )^{ 2} \div \: (\frac{3}{5} )^{ 2} + \frac{5}{3} = \\ \\ (\frac{3}{5} )^{ 2} \times (\frac{5}{3} )^{ 2} + \frac{5}{3} = \\ \\ \frac{9 \times 25}{25 \times 9} + \frac{5}{3} = 1 + \frac{5}{3} \\ \underline{\boxed{ ans = \frac{5}{3}}} \\ \\ \underline{ \boxed{solution....(b)}} \\ \\ ( \frac{x}{y})^{ - 2} × ( \frac{x}{y})^{ 4} × ( \frac{y}{x})^{ - 1} = \\ \\ ( \frac{x}{y})^{ - 2} × ( \frac{x}{y})^{ 4} × ( \frac{x}{y})^{ - 1} \\ since \: the \: two \: bases \: are \: same \to \\ ( \frac{x}{y})^{ - 2} ×( \frac{x}{y})^{(4 + ( - 1)} = \\ \\ ( \frac{y}{x})^{2} ×( \frac{x}{y})^{3} = \frac{ {y}^{2} \times {x}^{3} }{ {x}^{2} \times {y}^{3} } = \frac{x}{y} \\ \\ \underline{ \boxed{ans = \frac{x}{y} }}[/tex]
