(2^3n+1 x 9^n + 8n x 3^2n+1 + 6^2n x 2^n+3) : 13

[2^(3n+1) × 9^n + 8^n × 3^(2n+1) + 6^(2n) × 2^(n+3)] : 13 =

=[2×2^(3n)×(3^2)^n + (2^3)^n×3×3^(2n) + 2^(2n)×3^(2n)×2^3×2^n] : 13 =

= [2×2^(3n)×3^(2n) + 3×2^(3n)×3^(2n) + 8×2^(3n)×3^(2n)] : 13 =

= [2^(3n)×3^(2n)×(2 + 3 + 8)] : 13 =

= 13 × 2^(3n)×3^(2n) : 13 =

= 2^(3n) × 3^(2n(

Răspuns:   72ⁿ

Explicație pas cu pas:

( 2³ⁿ⁺¹ x 9ⁿ + 8ⁿx 3²ⁿ⁺¹ + 6²ⁿx 2ⁿ⁺³ ) : 13 =

= ( 2³ⁿ x 2¹ x 9ⁿ + 8ⁿx 3²ⁿ x 3¹ + (2x3)²ⁿx 2ⁿx 2³ ) : 13 =

= ( 8ⁿ x 2 x 9ⁿ + 8ⁿ x 9ⁿ x 3 + 2²ⁿ x 3²ⁿ x 2ⁿx 8 ) : 13 =

= [ ( 8 x 9)ⁿ x 2 + ( 8 x 9)ⁿ x 3 + ( 2²ⁿx2ⁿ) x 9ⁿx 8 ) : 13 =

= ( 72ⁿ x 2 + 72ⁿx 3 + 2³ⁿx 9ⁿ x 8 ) : 13 =

= ( 72ⁿ x 2 + 72ⁿ x 3 + 8ⁿ x 9ⁿ x 8 ) : 13 =

= 72ⁿ x ( 2 + 3 + 8 ) : 13 =

= 72ⁿ x 13 : 13 =

= 72ⁿ

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2²ⁿ x 2ⁿ = 2²ⁿ⁺ⁿ = 2³ⁿ = (2³)ⁿ = 8ⁿ

3²ⁿ = 3²ˣⁿ = ( 3²)ⁿ = 9ⁿ