Simplify.
#(-3r^2w^4)^3(2rw)^2(-3r^2)^3(4rw^2)^3(2r^2w^3)^4#
Apply the exponent power rule: #(a^m)^n=a^(m*n)#
Simplify #(-3r^2w^4)^3# to #(-3^3r^(2*3)w^(4*3))#.
#(-3^3r^(2*3)w^(4*3))(2rw)^2(-3r^2)^3(4rw^2)^3(2r^2w^3)^4#
Simplify #(2rw)^2# to #(2^2r^2w^2)#.
#(-3^3r^(2*3)w^(4*3))(2^2r^2w^2)(-3r^2)^3(4rw^2)^3(2r^2w^3)^4#
Simplilfy #(-3r^2)^3# to #(-3^3r^(2*3))#.
#(-3^3r^(2*3)w^(4*3))(2^2r^2w^2)(-3^3r^(2*3))(4rw^2)^3(2r^2w^3)^4#
Simplify #(4rw^2)^3# to #(4^3r^3w^(4*3))#.
#(-3^3r^(2*3)w^(4*3))(2^2r^2w^2)(-3^3r^(2*3))(4^3r^3w^(4*3))(2r^2w^3)^4#
Simplify #(2r^2w^3)^4# to #(2^4w^(3*4))#.
#(-3^3r^(2*3)w^(4*3))(2^2r^2w^2)(-3^3r^(2*3))(4^3r^3w^(2*3))(2^4r^(2*4)w^(3*4))#
Simplify.
#(-27r^6w^12)(4r^2w^2)(-27r^6)(64r^3w^6)(16r^8w^12)#
Take out the constants.
#-27xx4xx-27xx64xx16(r^6w^12r^2w^2r^6r^3w^6r^8w^12)#
Simplify #-27xx4xx-27xx64xx16# to #2985984#.
#2985984(r^6w^12r^2w^2r^6r^3w^6r^8w^12)#
Collect like variables.
#2985984(r^6r^2r^6r^3r^8w^12w^2w^6w^12)#
Apply exponent product rule: #a^ma^n=a^(a+n)#
#2985984(r^(6+2+6+3+8)w^(12+2+6+12))#
Simplify.
#2985984r^25w^32#
