(5¹×5²×5³×....×5²⁰⁰⁹):5²⁰⁰¹⁰⁰⁰=
=5¹⁺²⁺³⁺...⁺²⁰⁰⁰:5²⁰⁰¹⁰⁰⁰=
=5(²⁰⁰⁰°²⁰⁰¹/2):5²⁰⁰¹⁰⁹⁹=
=5¹⁰⁰⁰°²⁰⁰¹:5²⁰⁰¹⁰⁰⁰=
=5²⁰⁰¹⁰⁰⁰:5²⁰⁰¹⁰⁰⁰=1
Răspuns:
Explicație pas cu pas:
5^1*5^2*5^3 *....*5^2000 = 5^(1+2+3+...+2000)
1 + 2 + 3 + ....+ 2000 = 2000*(1 + 2000)/2 = 1000*2001 = 2001000
5^(1+2+3+...+2000) = 5^2001000
5^2001000 : 5^2001000 = 5^(2001000 - 2001000) = 5^0 = 1
