Вправи 201 - 342 » 271

271. Знайдіть значення виразу: 1) 8–3 • 27 = (23)–3 • 27 = 2–9 • 27 = 2–2 = 1/4; 2) 27–2 : 9–4 = (З3)–2 : (З2)–4 = 3–6 : З–8 = а–6–(–8) = З2 = 9; 3) 100–2 : 1000–5 • 0,016 = (102)–2 : (103)–5 • (10–2)6 = 10–4 : 10–15 • 10–12 = 10–4–(–15)+(–12) = 10–1 = 0,1; 4) (21/4)–4 • ((2/3)3)–3 = (9/4)–4 • (2/3)–9 = ((3/2)2)–4 • (2/3)–9 = (3/2)–8 • (2/3)–9 = (2/3)8 • (3/2)9 = (2/3)8 • (3/2)8 • 3/2 = (3/2 • 3/2)8 • 3/2 = 3/2; 5) 25–4 : (0,2–3)–2 = (52)–4 : (1/5)6 = 5–8 : 5–6 = 5–8–(–6) = 5–2 = 1/5^2 = 1/25; 6) ((-36)^(-3) • 6^8)/(216^(-5) • (-6)^18 ) = ((-6^2 )^(-3) • 6^8)/((6^3 )^(-5) • (-6)^18 ) = (〖-6〗^(-6) • 6^8)/(6^(-15) • 6^18 ) = 〖-6〗^2/6^3 = –1/6; 7) 6^(-10)/(81^(-2) • 16^3 ) = ((2 • 3)^(-10))/((3^4 )^(-2)• (2^4 )^(-3) ) = (2^(-10) • 3^(-10))/(3^(-8) • 2^(-12) ) = 2^2/3^2 = 4/9; 8) (14^5 • 2^(-7))/(28^(-2) • 7^8 ) = (2^5 • 7^5 〖 • 2〗^(-7))/(2^(-2) • 2^(-2) • 7^(-2)• 7^8 ) = 2^2/7 = 4/7.