How do you simplify #(-3d^2f^3g)^2[(-3d^2f)^3]^2#?

1 Answer

Answer:

#color(red)(3^8d^16f^12g^2#

Explanation:

#(-3d^2f^3g)^2=(-3)^2*(d^2)^2*(f^3)^2*g^2#
#=3^2*d^4*f^6*g^2# #color(red)("factor 1")#

#[((-3)*d^2*f^3)^3]^2=[(-3)^3*(d^2)^3*f^3*]^2#
#=[(-3)^3*d^6*f^3]^2=((-3^6)*d^12*f^6)#
#=3^6*d^12*f^6)# #color(red)("factor 2")#

Multiplying #color(red)("factors" (1) and (2))#
#3^2*d^4*f^6*g^2*3^6*d^12*f^6#
#=color(red)(3^8*d^16*f^12*g^2)#