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

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Answer 1 · 2017-10-07T17:40:18

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

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

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

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

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