Drastic times, with alien soldiers around (7)

I believe the answer is:

extreme

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'drastic' is the definition.
(thesaurus)

'times with alien soldiers around' is the wordplay.
'times with' becomes 'x' (multiplication sign. I am not sure about the 'with' bit.**).
'alien' becomes 'et' (extra terrestrial).
'soldiers' becomes 'reme' (Royal Electrical and Mechanical Engineers corps).
'around' means one lot of letters goes inside another.
'et'+'reme'='etreme'
'x' put into 'etreme' is 'EXTREME'.

Can you help me to learn more?

(Other definitions for extreme that I've seen before include "Far from moderate" , "Very intense - way-out" , "Utmost; excessive" , "sheer" , "Going beyond moderation" .)

I've seen this clue in The Independent.

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