Question

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

Answer 1

`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)`