First, simplify the #x# terms within the parenthesis using this rule for exponents: #x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))#
#((3x^color(red)(4))/(5x^color(blue)(2)))^2 = ((3x^(color(red)(4)-color(blue)(2)))/5)^2 = ((3x^2)/5)^2#
Now, we use these two rules of exponents to complete the simplification:
#a = a^color(red)(1)# and #(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))#
#((3x^2)/5)^2 = ((3^color(red)(1)x^color(red)(2))/5^color(red)(1))^color(blue)(2) = ((3^(color(red)(1)xxcolor(blue)(2))x^(color(red)(2)xxcolor(blue)(2)))/5^(color(red)(1)xxcolor(blue)(2))) = (3^2x^4)/5^2 = (9x^4)/25#
