First, use this rule of exponents to rewrite the expression:
#a = a^color(red)(1)#
#((3m^5r^3)/(4p^8))^4 => ((3^color(red)(1)m^5r^3)/(4^color(red)(1)p^8))^4#
Next, use this rule of equations to complete the simplification:
#(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))#
#((3^color(red)(1)m^5r^3)/(4^color(red)(1)p^8))^4 => ((3^color(red)(1)m^color(red)(5)r^color(red)(3))/(4^color(red)(1)p^color(red)(8)))^color(blue)(4) => (3^(color(red)(1) xx color(blue)(4))m^(color(red)(5) xx color(blue)(4))r^(color(red)(3) xx color(blue)(4)))/(4^(color(red)(1) xx color(blue)(4))p^(color(red)(8) xx color(blue)(4))) =>#
#(3^4m^20r^12)/(4^4p^32) => (81m^20r^12)/(256p^32)#
