Question

2 la puterea 102 - 2 la puterea 101 - 2 la puterea 100 - 2 la puterea 99

Answer 1

$\text{Dam factor comun puterea cea mai mica :}\\2^{102}-2^{101}-2^{100}-2^{99}=2^{99}(2^{3}-2^2-2-1)=2^{99}(8-4-2-1)= 2^{99}$

Answer 2

2^102 - 2^101 - 2^100 - 2^99 =

2^99 × ( 2^3 - 2^2 - 2^1 - 1) =

2^99 × ( 8 - 4 - 2 - 1 ) =

2^99 × 1 =

2^99
_____

^ = puterea

2^99 = 2 la puterea 99