Question

explicatimi si mie cum fac exercitiul
3 la puterea20-(8 la puterea15 : 4 la puterea 20-2 la puterea)tot ce este in paranteza la puterea 20 : 16 la puterea15

Answer 1

[tex]A=3^{20}-(8^{15}:4^{20}-2)^{20}:16^{15}\\ \text{ Trebuie sa stim urmatoarele reguli de calcul cu puteri:}\\ a^m:a^n=a^{m-n}\\ (a^m)^n=a^{mn}\\ (ab)^m=a^mb^m\\ (8^{15}:4^{20}-2)^{20}=[(2^3)^{15}:(2^2)^{20}-2^3]^{20}=(2^{45}:2^{40}-2^3)^{20}=\\ =(2^{45-40}-2^3)^{20}=(2^{5}-2^3)^{20}=(32-8)^{20}=24^{20}=(3\cdot2^3)^{20}=\\ 3^{20}\cdot2^{60}\\ A=3^{20}-3^{20}\cdot2^{60}:16^{15}=3^{20}-3^{20}\cdot2^{60}:(2^4)^{15}=\\ 3^{20}-3^{20}\cdot2^{60}:2^{60}=3^{20}-3^{20}=0 [/tex]