First, rewrite the expression as:
(8.6 xx 3.9)/(3.6 xx 4.3) xx (10^-3 xx 10^-6)/(10^-7 xx 10^-3) =>
(2 xx 4.3 xx 3 xx 1.3)/(3 xx 1.2 xx 4.3) xx (10^-3 xx 10^-6)/(10^-7 xx 10^-3) =>
(2 xx color(red)(cancel(color(black)(4.3))) xx color(blue)(cancel(color(black)(3))) xx 1.3)/(color(blue)(cancel(color(black)(3))) xx 1.2 xx color(red)(cancel(color(black)(4.3)))) xx (color(green)(cancel(color(black)(10^-3))) xx 10^-6)/(10^-7 xx color(green)(cancel(color(black)(10^-3)))) =>
(2 xx 1.3)/(1.2) xx 10^-6/10^-7 =>
(2 xx 1.3)/(2 xx 0.6) xx 10^-6/10^-7 =>
(color(red)(cancel(color(black)(2))) xx 1.3)/(color(red)(cancel(color(black)(2))) xx 0.6) xx 10^-6/10^-7 =>
2.1bar6 xx 10^-6/10^-7
Now, use this rule of exponents to evaluate the 10s terms:
x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))
2.1bar6 xx 10^color(red)(-6)/10^color(blue)(-7) =>
2.1bar6 xx 10^(color(red)(-6)-color(blue)(-7)) =>
2.1bar6 xx 10^(color(red)(-6)+color(blue)(7)) =>
2.1bar6 xx 10^1
Or
2.1bar6 xx 10
Or
21.bar6