Question

daca n eN*, simplificati:
a) 17 la puterea n + 17 la puterea n+ 1 pe 7 la puterea n + 7 la puterea n+1
b) 36x 6 la puterea n - 2 la puterea n +2 x3 la puterea n +1 - 2 la puterea n +1 x 3 la puterea n +2 pe 36 x 6 la puterea n - 6x6 la puterea n - 21 x 6 la puterea n

Answer 1

a) (17 ⁿ + 17 ⁿ⁺¹) / (7ⁿ+ 7 ⁿ⁺¹)=
=17 ⁿ(17⁰ + 17) / 7ⁿ(7⁰+ 7¹)=
=17 ⁿ × 18 / 7ⁿ ×8=
=17 ⁿ × 9 / 7ⁿ ×4


 b) (36x 6ⁿ - 2ⁿ⁺² x3ⁿ⁺¹ - 2ⁿ⁺¹x 3ⁿ⁺²)/(36 x 6ⁿ- 6x6ⁿ - 21 x 6ⁿ)=
=(36x 6ⁿ - 2ⁿx2² x3ⁿx3 - 2ⁿx2x 3ⁿx3²)/(36 x 6ⁿ- 6x6ⁿ - 21 x 6ⁿ)=
=(36x 6ⁿ - 2² x3x6ⁿ - 2x3²x 6ⁿ)/(36 x 6ⁿ- 6x6ⁿ - 21 x 6ⁿ)=
=3x6ⁿ(12 - 2²  - 2x3)/3x6ⁿ(12- 2 -7 )=
=3x6ⁿx2/3x6ⁿx3=
=2/3