using Tetration, we can get much larger than the simple exponentiation..
Move the top and bottom matchstick from the zero in the ten's place, and form a subscript "11" after the resulting "61111110" to form:
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Or: (provided you can ignore the incorrect relative font size between the intended superscript vs regular size)
I'm not sure it would be reasonable to even try to determine how long this would be in digits, as it is equivalent to:
1111...11 (61,111,110 11's)
*edit: thanks to @Phlarx for catching the 7->11 I probably should have thought of that.. just realized I could swap the position of the sub / superscript to get many more exponentiation iterations vs. larger starting number (which quickly pays off)