First, use these two rules of exponents to simplify the exponents outside the parenthesis:
#a = a^color(red)(1)# and #(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))#
#(a^4b)^7(a^5b^7)^3 => (a^color(red)(4)b^color(red)(1))^color(blue)(7)(a^color(red)(5)b^color(red)(7))^color(blue)(3) =>#
#(a^(color(red)(4) xx color(blue)(7))b^(color(red)(1) xx color(blue)(7)))(a^(color(red)(5) xx color(blue)(3))b^(color(red)(7) xx color(blue)(3))) => (a^28b^7)(a^15b^21)#
We can rewrite this expression as:
#(a^28a^15)(b^7b^21)#
We can use this rule for exponents to simplify the #a# and #b# terms:
#x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))#
#(a^color(red)(28)a^color(blue)(15))(b^color(red)(7)b^color(blue)(21)) => a^(color(red)(28) + color(blue)(15))b^(color(red)(7) + color(blue)(21)) => a^43b^28#
