Răspuns:
Explicație pas cu pas:
a) 3ⁿ x 3ⁿ⁺¹ x 3ⁿ⁺² = 3⁽ⁿ⁺ⁿ⁺¹⁺ⁿ⁺²⁾ = 3³ⁿ⁺³ = 3³⁽ⁿ⁺¹⁾ = 27ⁿ⁺¹
_______________________________________
b) 2¹x2²x2³x........x2²⁰ =
= 2⁽¹⁺²⁺³⁺......⁺²⁰⁾ =
= 2⁽²⁰ˣ²¹:²⁾ =
= 2²¹⁰
1+2+3+.......+20 = 20 x(1+20):2 = 21x10 = 210 aplic formula sumei lui Gauss
________________________________________________
c) 4¹ x 4²x4³x ......x4⁵⁰ =
= 4⁽¹⁺²⁺³⁺........⁺⁵⁰⁾ =
= 4⁽⁵⁰ˣ⁵¹:²⁾ =
= 4¹²⁷⁵
1+2+3+......+50 = 50 x( 1+50): 2 = 50x51:2=2550:2=1275
_______________________________________________
d) [(2³)⁴ ]⁵ : 2⁵⁰ = 2⁽³ˣ⁴ˣ⁵⁾ : 2⁵⁰ = 2⁽⁶⁰⁻⁵⁰⁾ = 2¹⁰
_____________________________________
e) [ (3⁵)¹⁰]² : (3⁴)²⁰ = 3⁽⁵ˣ¹⁰ˣ²⁾ : 3⁽⁴ˣ²⁰⁾ = 3⁽¹⁰⁰⁻⁸⁰⁾ = 3²⁰ = 3²ˣ¹⁰ = 9¹⁰
