Post Undeleted by garej
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FullSimplifySimplify /@ Expand@exprExpand @ expr /. Sqrt[c d] / (c d)^2 -> 1/(c d)^(3/2),

where expr = (-a^3 (-1 + b^2) - 3 a b^2 (2 + b^2) d c)/(b^2 (d c)^(3/2))

Result

enter image description here

FullSimplify /@ Expand@expr /. Sqrt[c d]/ (c d)^2 -> 1/(c d)^(3/2),

where expr = (-a^3 (-1 + b^2) - 3 a b^2 (2 + b^2) d c)/(b^2 (d c)^(3/2))

Result

enter image description here

Simplify /@ Expand @ expr /. Sqrt[c d] / (c d)^2 -> 1/(c d)^(3/2),

where expr = (-a^3 (-1 + b^2) - 3 a b^2 (2 + b^2) d c)/(b^2 (d c)^(3/2))

Result

enter image description here

    Post Deleted by garej
1
source | link

FullSimplify /@ Expand@expr /. Sqrt[c d]/ (c d)^2 -> 1/(c d)^(3/2),

where expr = (-a^3 (-1 + b^2) - 3 a b^2 (2 + b^2) d c)/(b^2 (d c)^(3/2))

Result

enter image description here