To represent the number 8857 in Roman numerals using the extended notation system, where a bar over a numeral indicates multiplication by 1000, we break it down as follows:

1. 8000: Represented as ‘V̅I̅I̅I̅’ (where ‘V̅’ stands for 5000 and ‘I̅I̅I̅’ adds up to 3000).
2. 800: Represented as ‘DCCC’ (‘D’ for 500 and ‘CCC’ for 300).
3. 50: Represented as ‘L’.
4. 7: Represented as ‘VII’.

Thus, 8857 in extended Roman numerals is written as: V̅I̅I̅I̅DCCCLVII.

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