First, use these two rules of exponents to eliminate the out exponents:
#a = a^color(red)(1)# and #(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))#
#(5x^3)^2 * (4x)^3 = (5^color(red)(1)x^color(red)(3))^color(blue)(2) * (4^color(red)(1)x^color(red)(1))^color(blue)(3) = #
#(5^(color(red)(1) xx color(blue)(2))x^(color(red)(3) xx color(blue)(2))) * (4^(color(red)(1) xx color(blue)(3))x^(color(red)(1) xx color(blue)(3))) =
(5^2x^6) * (4^3x^3) = (25x^6) * (64x^3)#
Next, rewrite the expression as:
#(25x^6) * (64x^3) = (25 * 64)(x^6 * x^3) = 1600(x^6 * x^3)#
Now, use this rule of exponents to complete the multiplication:
#x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))#
#1600(x^6 * x^3) = 1600(x^color(red)(6) xx x^color(blue)(3)) = 1600x^(color(red)(6) + color(blue)(3)) = 1600x^9#
