Hello.
I believe this is just conversion factors.
*I think the 107 above means 10^7
1.27 * 10^7 mol * 6.01 kJ/ 1 mol = 76,327,000 kJ
That value, rounded to significant figures, produces 763 * 10^5 kJ
*The 1.27 and 6.01 represent the least amount of significant figures; the rule of sig. figs. for division and multiplication is the value with the fewest sig. figs..
(For addition and subtraction, the least amount of decimal places determines the number of sig. figs..)
Leave a comment if you have a question. Good luck!