How do you simplify #(-3r^2w^4)^3(2rw)^2(-3r^2)^3(4rw^2)^3(2r^2w^3)^4#?

1 Answer
Jan 9, 2018

Answer:

#(-3r^2w^4)^3(2rw)^2(-3r^2)^3(4rw^2)^3(2r^2w^3)^4=2985984r^25w^32#

Explanation:

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#