Question

(4^31+6x32^12-5x16^15):(8^21-5x8^20)-1
Va rog cat mai repede!

Answer 1

   
[tex](4^{31}+6\times32^{12}-5\times16^{15}):(8^{21}-5\times8^{20})-1=\\\\ =[(2^2)^{31}+6\times(2^5)^{12}-5\times(2^4)^{15}]:[(2^3)^{21}-5\times (2^3)^{20}]-1=\\\\ =[2^{2\times31}+6\times 2^{5\times12}-5\times2^{4\times15}]:[2^{3\times21}-5\times 2^{3\times20}]-1=\\\\ =[2^{62}+6\times 2^{60}-5\times2^{60}]:[2^{63}-5\times 2^{60}]-1=\\\\ =[2^{2+60}+6\times 2^{60}-5\times2^{60}]:[2^{3+60}-5\times 2^{60}]-1= \\ \\ =[2^2\times2^{60}+6\times 2^{60}-5\times2^{60}]:[2^3 \times 2^{60}-5\times 2^{60}]-1= [/tex]


[tex]=[4\times2^{60}+6\times 2^{60}-5\times2^{60}]:[8 \times 2^{60}-5\times 2^{60}]-1= \\ \\ =2^{60}(4+6-5): 2^{60}[8 -5)-1= \\ \\ \displaystyle = \frac{2^{60}(4+6-5)}{2^{60}[8 -5)} -1 =\frac{2^{60} \times 5}{2^{60}\times 3} -1 = \frac{5}{3} - 1 = \frac{5-3}{3}= \boxed{ \frac{2}{3}}[/tex]