Question

Comparati numerelr a= $5^{30}$ si b= $7^{20}$ .
Aratati ca numarul $3^{45}$ + $3^{44}$ + $3^{43}$  se imparte exact la 13.
Daca ( 2 × 9) totul la 35 = $2^{35}$ ×$3^{a}$ atunci determinati valoarea numarului natural a.

Answer 1

[tex]1)a=5^{30}=(5^3)^{10}=125^{10}\\ b=7^{20}=(7^2)^{10}=49^{10}\\ a>b\\ 2)3^{43}(3^2+3^1+3^0)=3^{43}\cdot13\\ 3^{43}\cdot13:13=3^{43}\\ 3)(2\cdot9)^{35}=2^{35}\cdot9^{35}=2^{35}\cdot(3^2)^{35}=2^{35}\cdot3^{70}=>a=70[/tex]