Вправи 301 - 400 » 390

390. Спростіть вираз: 1) (x/y)–5 • (y/x)–5 = (x/y • y/x)–5 = 1–5 = 1; 2) (x/(y+2))–1 • ((y+2)/x)–1 = (x/(y+2) • (y+2)/x)–1 = 1–1 = 1; 3) (a/(a+ b))–3 • ((a+ b)/b)–3 = ((a•(a+ b))/((a+ b)•b))–3 = (a/b)–3; 4) (z – 6)–8 • (z/(z-6))–8 = (((z-6)•z)/(z-6))–8 = z–8; 5) (n + 5)–7 • (n/(n+5))–7 • (1/n)–7 = (((n+5)•n)/((n+5)• n))–7 = 1–7 = 1; 6) (1/(b+ c))–1 : (2/(b+ c))–1 = b + c : (b+ c)/2 = b + c • 2/(b+2) = 2; 7) (a/bc)–6 : (a^2/bc)–6 = a^(-6)/(b^(-6) c^(-6) ) : (bc/a^2 )6 = a^(-6)/(b^(-6) c^(-6) ) : (b^6 c^6)/a^12 = a^(-6)/(b^(-6) c^(-6) ) • a^12/(b^6 c^6 ) = a6; 8) n^(-5)/m^(-5) : (m^6/〖2n〗^(-4) )–5 = n^(-5)/m^(-5) : m^(-30)/(2^(-5) n^20 ) = n^(-5)/m^(-5) • (2^(-5) n^20)/m^(-30) = 1/32n15m35.