Вправи 301 - 400 » 400

400. Спростіть вираз: 1) 1/(〖9n〗^45 m^(-35) ) • m^(-20)/n^(-30) = m^(-20)/(〖9n〗^15 m^(-35) ) = 1/9m15n–15; 2) 5ba0 • a^5/〖4b〗^(-3) = (5b •1 • a^5)/〖4b〗^(-3) = 1,25a5b4; 3) 〖2b〗^(-8)/〖3a〗^2 • 0,6b–1a–9 = 〖2b〗^(-8)/〖3a〗^2 • (〖6b〗^(-1) a^(-9))/10 = (〖2b〗^(-9) a^(-9))/〖5a〗^2 = 0,4a–11b–9; 4) 5xyz • 〖2x〗^(-2)/(〖5y〗^6 z^(-11) ) = 〖5xyz •2x〗^(-2)/(〖5y〗^6 z^(-11) ) = 2x–1y–5z12; 5) 〖2x〗^(-4)/y^(-2) • 0,1xy–5 = 〖2x〗^(-4)/y^(-2) • xy^(-5)/10 = (x^(-3) y^(-5))/〖5y〗^(-2) = 0,2x–3y–3; 6) ((a–2 • a2)–5 • a2)–1 = ((a0)–5 • a2)–1 = ((1)–5 • a2)–1 = (1 • a2)–1 = a–2; 7) ((x0 • x–7)–5 • x–1)10 = ((1 • x–7)–5 • x–1)10 = (x35 • x–1)10 = (x34)10 = x340; 8) ((a–1 • a)–1 • a)–1 • a = ((a0)–1 • a)–1 • a = (1 • a)–1 • a = a–1 • a = a0 = 1; 9) ((x–9 : x–1)–1 : x7) : x0 = ((x–8)–1 : x7) : 1 = x8 : x7 = x; 10) (((a–3)–1 • b3)–4a12)2 • b20 = ((a3 • b3)–4 • a12)2 • b20 = (a–12b–12a12)2 • b20 = (a0b–12)2 • b20 = (1 • b–12)2 • b20 = b–24• b20 = b–4.