First, use this rule of exponents to rewrite the expression:
#a = a^color(red)(1)#
#((3xy^3)/(2z))^2 => ((3^color(red)(1)x^color(red)(1)y^3)/(2^color(red)(1)z^color(red)(1)))^2#
Now, use this rule of exponents to complete the simplification:
#(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))#
#((3^color(red)(1)x^color(red)(1)y^color(red)(3))/(2^color(red)(1)z^color(red)(1)))^color(blue)(3) => (3^(color(red)(1) xx color(blue)(3))x^(color(red)(1) xx color(blue)(3))y^(color(red)(3) xx color(blue)(3)))/(2^(color(red)(1) xx color(blue)(3))z^(color(red)(1) xx color(blue)(3))) =>#
#(3^3x^3y^9)/(2^3z^3) => (27x^3y^9)/(8z^3)#
