Вправи 301 - 400 » 363

363. Обчисліть: 1) (8^(-4)• 6^10+ 27^3)/(10^0• 81^3- 18^6• 6^(-3) ) • (7/19)–1 = (〖(2〗^3 )^(-4)• 2^10• 3^10+ 3^9)/(1 • 3^12- 3^6• 6^6 • 6^(-3) ) • 19/7 = (3^9•(2^(-2)•3+1))/(3^6•(3^6- 6^3)) • 19/7 = (3^3•1 3/4)/(3^6- 3^3 • 2^3 ) • 19/7 = (27 • 7/4)/(3^3•(3^3- 2^3)) • 19/7 = (27 •7)/(27 •4 •(27-8)) • 19/7 = 7/(4 •19) • 19/7 = 1/4 = 0,25; 2) (4^(-8) • 〖0,0001〗^(-5)+ 125^6 •(3 1/3 )^2)/(〖(0,2〗^10 )^(-2)+ 3^(-2)• 50^10 • 〖0,5〗^12 ) = (4^(-8)• 10000^5+ 〖(5〗^3 )^6•(10/3 )^2)/(〖0,2〗^(-20)+ 3^(-2)• 2^10 • 25^10 •(1/2 )^12 ) = (〖(2〗^3 )^(-8) • 10000^5+ 5^18• 100/9)/((1/5 )^(-20)+ 1/9 • 2^10• 〖(5〗^2 )^10• 1/2^12 ) = (2^(-24)• 〖(10〗^4 )^5+ 5^18• 100/9)/(5^20+ 5^20/2^2 • 1/9) = (2^(-24)• 10^20+ 5^18• 100/9)/(5^20•(1+ 1/36)) = (2^(-24) • 2^20• 5^20+ 5^18 • 100/9)/(5^20 •1 1/36) = (5^18•(2^(-4)• 5^2+ 100/9))/(5^20 • 37/36) = (1/16 •25+ 100/9)/(5^2 • 37/36) = (25/16+ 100/9)/((25 •37)/36) = (25 •(1/16+ 4/9))/(25 • 37/36) = ((9+16)/144)/(37/36) = = 25/144 : 37/36 = 25/144 • 36/37 = 25/148.