First, we can use this rule of exponents to simplify the #x# terms within the parenthesis:
#x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))#
#((2x^color(red)(0)y^3)/(x^color(blue)(-1)y^4))^3 =>#
#((2x^(color(red)(0)-color(blue)(-1))y^3)/y^4)^3 =>#
#((2x^(color(red)(0)+color(blue)(1))y^3)/y^4)^3 =>#
#((2x^1y^3)/y^4)^3#
Next, use this rule of exponents to simplify the #y# term within the parenthesis:
#x^color(red)(a)/x^color(blue)(b) = 1/x^(color(blue)(b)-color(red)(a))#
#((2x^1y^color(red)(3))/y^color(blue)(4))^3 =>#
#((2x^1)/y^(color(blue)(4)-color(red)(3)))^3 =>#
#((2x^1)/y^1)^3#
Use this rule of exponents to rewrite the constant:
#a = a^color(red)(1)#
#((2^1x^1)/y^1)^3#
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))#
#((2^color(red)(1)x^color(red)(1))/y^color(red)(1))^color(blue)(3) =>#
#(2^(color(red)(1)xxcolor(blue)(3))x^(color(red)(1)xxcolor(blue)(3)))/y^(color(red)(1)xxcolor(blue)(3)) =>#
#(2^3x^3)/y^3 =>#
#(8x^3)/y^3#
