(99)¹⁰⁰ > (100)⁹⁹

Because,

(100)⁹⁹ = (99+1)⁹⁹

= ⁹⁹C₀ (99)⁹⁹ + ⁹⁹C₁(99)⁹⁸ + ....................... + 1

= (99)⁹⁹ + (99).(99)⁹⁸ +............... + 1

= 2.(99)⁹⁹ + terms relatively much smaller terms

and this is much smaller than 99.(99)⁹⁹ i.e (99)¹⁰⁰