Question

(3^202x3^3+3^303:3^98+9^100x3^5):3^205-1^2013

Answer 1

(3^202x3^3+3^303:3^98+9^100x3^5):3^205-1^2013 = 
(3^205+3^205+(3^2)^100x3^5):3^205-1 = 
(3^205+3^205+3^205):3^205-1 = 
(3*3^205):3^205-1=
3^206:3^205-1=
3^1-1=
3-1=
2

Answer 2

Analizăm expresia din paranteză:

[tex]\it 3^{202}\cdot3^3 =3^{202+3} =3^{205} \\\;\\ 3^{303} : 3^{98} = 3^{303-98} =3^{205} \\\;\\ 9^{100}\cdot3^5=(3^2)^{100}\cdot3^5 = 3^{200}\cdot3^5 =3^{205}[/tex]

Acum, exercițiul devine:

[tex]\it (3^{205}+3^{205}+3^{205}):3^{205} - 1^{2013}=3\cdot3^{205}:3^{205} -1 = \\\;\\ =3^{206} :3^{205} -1 = 3^{206-205} -1 =3^1-1 = 3-1 = 2[/tex]