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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.
1 2
Comments  
TRICK: Avoid apostrophes whenever possible.

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.
To avoid fussiness, I think it's best to use the attributive sense wherever possible. This isn't grammatically possible before a superlative ("hottest", "biggest" etc.), so the apostrophe in those examples seems necessary. I do not see any need for an apostrophe in any of your examples 1-9.
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Mr. Wordy,

Does it matter if the superlative precedes or follows the listed decade? In other words, if comes before or after (see examples below), do we still use the apostrophe, regardless?

The hottest 1970s' group was arguably the Bee Gees. GOOD?
The 1970s' hottest group was arguably the Bee Gees. GOOD?

The biggest 1980s' wrestler was Hulk Hogan. GOOD?

The 1980s' biggest wrestler was Hulk Hogan. GOOD?

Thanks, all.
Mr W means this, I'm sure:

The hottest 1970s group was arguably the Bee Gees.
The 1970s' hottest group was arguably the Bee Gees.

The biggest 1980s wrestler was Hulk Hogan.

The 1980s' biggest wrestler was Hulk Hogan.
victoThe hottest 1970s' group was arguably the Bee Gees. GOOD?
The biggest 1980s' wrestler was Hulk Hogan. GOOD?
The 1980s' biggest wrestler was Hulk Hogan. GOOD?

Or should I just simply omit the apostrophes in these as well?
You can't use the attributive sense (and hence you need an apostrophe) when the superlative immediately follows the decade. Your first two examples do not fall into that category and do not need apostrophes. The third does if you must write it that way. Some people (including me) may stylistically prefer to write the sentence a different way (e.g. "The biggest wrestler of the 1980s...").
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Victo, it seems you amended your post while I was replying to it. Hopefully everything still makes sense.
Mister MicawberMr W means this, I'm sure:

The hottest 1970s group was arguably the Bee Gees.
The 1970s' hottest group was arguably the Bee Gees.
The biggest 1980s wrestler was Hulk Hogan.
The 1980s' biggest wrestler was Hulk Hogan.
Yup.
So, then, if a instead of the preceded each, we'd do the same thing, then, right? Agree with the examples below? Thanks a mil once again. Emotion: smile

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

A big 1980s wrestler was Hulk Hogan.

A 1980s' big-time wrestler was Hulk Hogan.
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