Question

(Am sa scriu ghilimele in locul
puterilor)Calculati:a)(9''10-9''9-9''8):71+(8''11-8''10-8''9):55-3''16-2''18;b)(3''n+2+3''2n+1-3''2n):3''2n;c)385''3-385''2x384-385x375;d)68''3-68''2x67-68x67.va rog,am nevoie de ajutor!

Answer 1

[tex]a)(9^{10}-9^9-9^8):71+(8^{11}-8^{10}-8^9):55-3^{16}-2^{18}=\\ 9^8(9^2-9-1):71+8^9(8^2-8-1):55-(3^2)^8-(2^3)^6=\\ 9^8*71:71+8^9*55:55-9^8-8^6=\\ 9^8+8^9-9^8-8^6=8^6(8^3-1)\\ b)(3^{2n+2}+3^{2n+1}-3^{2n}):3^{2n}=\\ (3^{2n}*3^2+3^{2n}*3-3^{2n}):3^{2n}=\\ 3^{2n}(3^2+3-1):3^{2n}=11\\ c)385^3-385^2*384-385*375=\\ 385^2(385-384)-385*375=\\ 385^2-385*375=\\ 385(385-375)=\\ 385*10=3850\\ d)68^3-68^2*67-68*67=\\ 68^2(68-67)-68*67=\\ 68^2-68*67=\\ 68(68-67)=68[/tex]