Monomials??

Simplify the following:
(-3 d^2 f^3 g)^2 ((-3 d^2 f)^3)^2

Multiply each exponent in -3 d^2 f^3 g by 2:
(-3)^2 d^(2×2) f^(2×3) g^2 ((-3 d^2 f)^3)^2

2×3 = 6:
(-3)^2 d^(2×2) f^6 g^2 ((-3 d^2 f)^3)^2

2×2 = 4:
(-3)^2 d^4 f^6 g^2 ((-3 d^2 f)^3)^2

(-3)^2 = 9:
9 d^4 f^6 g^2 ((-3 d^2 f)^3)^2

Multiply each exponent in -3 d^2 f by 3:
9 d^4 f^6 g^2 (-3)^3 d^(3×2) f^3^2

3×2 = 6:
9 d^4 f^6 g^2 ((-3)^3 d^6 f^3)^2

(-3)^3 = (-1)^3×3^3 = -3^3:
9 d^4 f^6 g^2 (-3^3 d^6 f^3)^2

3^3 = 3×3^2:
9 d^4 f^6 g^2 (-3×3^2 d^6 f^3)^2

3^2 = 9:
9 d^4 f^6 g^2 (-3×9 d^6 f^3)^2

3×9 = 27:
9 d^4 f^6 g^2 (-27 d^6 f^3)^2

Multiply each exponent in -27 d^6 f^3 by 2:
9 d^4 f^6 g^2×(-27)^2 d^(2×6) f^(2×3)

2×3 = 6:
9×(-27)^2 d^4 f^6 g^2 d^(2×6) f^6

2×6 = 12:
9×(-27)^2 d^4 f^6 g^2 d^12 f^6
9×729 d^4 f^6 g^2 d^12 f^6

9 d^4 f^6 g^2×729 d^12 f^6 = 9 d^(4+12) f^12 g^2×729:
9×729 d^(4+12) f^12 g^2

4+12 = 16:
9×729 d^16 f^12 g^2

9×729 = 6561:
Answer: |6561 d^16 f^12 g^2

Hello MamaLlama,  I haven't seen you for ages.  Welcome back!           

(-3d2f3g)2[(-3d2f)3]2

$(-3d^2f^3g)^2[(-3d^2f)^3]^2\\ =(-3d^2f^3g)^2\quad[(-3d^2f)^3]^2\\ =((-3)^2d^{2*2}f^{3*2}g^2)\quad(-3d^2f)^{3*2}\\ =9d^{4}f^{6}g^2\qquad\qquad(-3d^2f)^6\\ =9d^{4}f^{6}g^2\qquad\qquad(-3)^6d^{2*6}f^6\\ =9d^{4}f^{6}g^2\qquad\qquad729d^{12}f^6\\ =9*729\quad d^{4+12}\quad f^{6+6}\quad g^2\\ =6561\: d^{16}\: f^{12}\:g^2\\ $

Just your d indice is wrong    :)