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Fie numarul natural A=[(3^3·3^4+3^6·3+3^2012:3^2005)·(27^3)^55]^4+1^2012



Răspuns :

A = [(3^3 × 3^4 + 3^6 × 3 + 3^2012 : 3^2005) × (27^3)^55]^4 + 1^2012 =

={(3^7 + 3^7 + 3^7) × [(3^3)^3]^55}^4 + 1 =

= [3×3^7 × (3^9)^55]^4 + 1 =

= (3^8 × 3^495)^4 + 1 =

= (3^503)^4 + 1 =

= 3^2012 + 1

Răspuns:

Explicație pas cu pas:

A=[(3^7+3^7+3^7)×(3^9)^55]^4+1==(3^8×3^495]^4+1=(3^503)^4+1=

=3^2012+1