Вправи 301 - 400 » 387

387. Спростіть вираз: 1) (m + n)3 • (m + n)–3 = (m + n)0 = 1; 2) (5 + a)–8 • (5 + a)5 = (5 + a)–3; 3) 〖(p+ m)〗^(-1)/〖(p+ m)〗^2 = (p + m)–1 • (p + m)–2 = (p + m)–3; 4) (m/n)–1 • (m/n)–5 = (m/n)–6 = m–6n6; 5) (a + b) • 〖(a+ b)〗^2/〖(a- b)〗^3 • (a – b)–2 = (a + b) • (a + b)2 • (a – b)–2 • (a – b)–2 = (a + b)3 • (a – b)–5 = 〖(a+ b)〗^3/〖(a- b)〗^5 ; 6) x^(-3)/〖(y+1)〗^0 • 〖(x+2)〗^0/x^(-1) = (x^(-3)•1)/(1• x^(-1) ) = x–3 • x = x–2; 7) 〖(y+5)〗^(-4)/y^10 • y^(-15)/〖(y+5)〗^(-8) = (〖(y+5)〗^(-4)•〖(y+5)〗^8)/(y^10• y^15 ) = 〖(y+5)〗^4/y^25 ; 8) 〖(n+4m)〗^(-1)/p^4 • p^3/〖(n+4m)〗^0 : 〖(n+4m)〗^(-10)/p = 〖(n+4m)〗^(-1)/p^4 • p^3/1 • p/〖(n+4m)〗^(-10) = (p^4•〖(n+4m)〗^10 )/(p^4•〖(n+4m)〗^1 ) = (n + 4m)9.