Question

15. Efectuati:
(4^31+6×32^12-5×16^15):(8^21 – 5-8^20)-1 ​

Answer 1

4^31 = (2^2)^31 =  2^62

32^12 = (2^5)^12 = 2^60

16^15 = (2^4)^15 = 2^60

(2^62+6×2^60-5×2^60):(8^21-5-8^20)-1 =

(2^62+2^60):(8^21-5-8^20)-1 =

2^60(2^2+1):(8^21-5-8^20)-1 =

5×2^60/(8^21-5-8^20) -1

Answer 2

Răspuns:

$\it (4^{31}+6\cdot32^{12}-5\cdot16^{15}):(8^{21}-5-8^{20})-1\\\\\\(2^{2\cdot31}+6\cdot (2^{5})^{12}-5\cdot (2^{4})^{15}):((2^{3})^{21}-5-(2^{3})^{20})-1\\\\\\(2^{62}+6\cdot 2^{60}-5\cdot 2^{60}):(2^{3\cdot21}-5-2^{3\cdot20})-1\\\\\\(2^{62}+2^{60}):(2^{63}-5-2^{60})-1\\\\\\2^{60}\cdot(2^{2}+1):(2^{63}-5-2^{60})-1\\\\\\2^{60}\cdot5:(2^{63}-5-2^{60})-1\\\\\\ \boxed{\it \dfrac{2^{60}\cdot5}{(2^{63}-5-2^{60})-1} }$