Writer rising in river left power unit (7)

I believe the answer is:

decibel

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'power unit' is the definition.
'decibel' can be an answer for 'unit' (decibel is a kind of unit). I am not sure about the 'power' bit.

'writer rising in river left' is the wordplay.
'writer' becomes 'bic' (kind of pen).
'rising' is a reversal indicator (going up in a down clue).
'in' indicates putting letters inside.
'river' becomes 'Dee' (River Dee).
'left' becomes 'l' (common abbreviation).
'bic' in reverse letter order is 'cib'.
'cib' going within 'dee' is 'decibe'.
'decibe'+'l'='DECIBEL'

Can you help me to learn more?

(Other definitions for decibel that I've seen before include "Unit relating to sound or power measurement" , "I relate to volume" , "Sound level unit" , "Unit of volume" , "Measure of sound" .)

I've seen this clue in The Sun.

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