To represent the number 6791 in Roman numerals using the extended system, where a bar over a numeral indicates multiplication by 1000, we break it down as follows:

1. 6000: Represented as ‘V̅I̅’ (where ‘V̅’ signifies 5000 and ‘I̅’ signifies 1000).
2. 700: Represented as ‘DCC’ (‘D’ for 500 and ‘CC’ for 200).
3. 90: Represented as ‘XC’ (‘X’ for 10 and ‘C’ for 100, but in this subtractive combination, it represents 90).
4. 1: Represented as ‘I’.

Combining these, 6791 in extended Roman numerals is written as: V̅I̅DCCXCI.

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