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TRICK: Those decades preceded by "the" and an "adjective" are most likely interpreted as possessive, so use the apostrophe after the decade.
  • The 1970s' greatest director was Martin Scorsese. The 1980s' hottestmodel was Christine Brinkley. It was the 1990s' hottest movie!
  • The term "Big Apple" was popularized by a 1970s tourism promotion campaign.
(No apostrophe after 1970s because "a" is used.)
  • The term "Big Apple" was popularized by the 1970s' biggest tourism promotion campaign. (Apostrophe after 1970s because "the" with an adjective is used after the decade.)
However, those preceded by "the" might be interpreted as possessives, in which case the writer may include the apostrophe. Again, my recommendation would be: If in doubt, assume it's attributive.

Do these look correct, then?

1. The term "Big Apple" was popularized by a 1970s tourism promotion campaign.
2. The term "Big Apple" was popularized by a seventies tourism promotion campaign.
3. The 1980s' band Huey Lewis and The News recorded a string of hits.
4. The eighties' band Huey Lewis and The News recorded a string of hits.
5. The 1970s' sitcom "Sanford and Son" had controversial racial content.
6. The seventies' sitcom "Sanford and Son" had controversial racial content.
7. The '90s' band Depeche Mode appealed to the urban community.
8. The nineties' band Depeche Mode appealed to the urban community.
9. A seventies fad was to wear wristbands.
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Comments  (Page 2) 
Good?
Nope.

A 1970s smokin' hot group was arguably the Bee Gees.

A 1980s big-time wrestler was Hulk Hogan.
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So if we do an inverted construction, would you agree with this? Thanks for all your help.

A smokin' hot 1970s group was arguably the Bee Gees.
A big-time 1980s wrestler was Hulk Hogan.

Thanks again. Truly appreciative of all your help.Emotion: big smile
Yes, those are OK. The use of 'arguably' in the first seems semantically odd: either off-register or overly hesitant. Or perhaps it's the overall structure: I would expect The Bee Gees were a smokin' hot '70s group. Hulk Hogan was a....

So I guess I don't like the inversion.