Question

(9^2×9^4×9^6×...×9^80)÷(3^1×3^2×3^3×3^
50)​

Answer 1

Salut! =)

( 9² × 9⁴ × 9⁶ × .... × 9⁸⁰ ) : ( 3 × 3² × 3³ × ... × 3⁵⁰ ) = ?

9² × 9⁴ × 9⁶ × .... × 9⁸⁰

9²⁽¹⁺²⁺³⁺    ⁺⁴⁰ )

1 + 2 + 3 + ... + 40 = $\frac{40 * 41 }{2}$ = 20 × 41 = 820

Folosim formula Sumei Gauss

1 + 2 + 3 + ... + n = $\frac{n ( n + 1 ) }{2}$

9²ˣ⁸²⁰ = 9¹⁶⁴⁰ = ( 3 ² ) ¹⁶⁴⁰ = 3³²⁸⁰

3 × 3² × 3³ × ... × 3⁵⁰

3¹⁺²⁺³⁺    ⁺⁵⁰  = 3¹²⁷⁵

1 + 2 + 3 + ... + 50 = $\frac{50 * 51 }{2}$ = 25 × 51 = 1275

3³²⁸⁰ : 3¹²⁷⁵ =  3³²⁸⁰⁻¹²⁷⁵ =  3²⁰⁰⁵

R : 3²⁰⁰⁵

Bafta! =)