71. Упростите выражение: 1) 5a⁶·(−3a²b)²; 2) (−x⁴y³)⁷·8x²y⁵; 3) (−0,1a²bc⁵)²·100bc⁴; 4) −1 3/5m⁴n³·(−1/2m³p⁶)³; 5) 2 1/4a⁵b·(2/3ab³)³; 6) (−5a³b⁷)³·(−1/5ac⁶)².

1. \(5a^6\cdot(-3a^2b)^2=5a^6\cdot9a^4b^2=45a^{10}b^2\).
2. \((-x^4y^3)^7\cdot8x^2y^5=-x^{28}y^{21}\cdot8x^2y^5=-8x^{30}y^{26}\).
3. \((-0.1a^2bc^5)^2\cdot100bc^4=0.01a^4b^2c^{10}\cdot100bc^4=a^4b^3c^{14}\).
4. \(-1\frac35=-\frac85\), а \(\left(-\frac12\right)^3=-\frac18\). Поэтому \(-\frac85\cdot\left(-\frac18\right)m^7n^3p^{18}=\frac15m^7n^3p^{18}\).
5. \(2\frac14=\frac94\), а \(\left(\frac23\right)^3=\frac8{27}\). Тогда \(\frac94\cdot\frac8{27}a^8b^{10}=\frac23a^8b^{10}\).
6. \((-5a^3b^7)^3=-125a^9b^{21}\), \(\left(-\frac15ac^6\right)^2=\frac1{25}a^2c^{12}\). Значит, \(-125\cdot\frac1{25}a^{11}b^{21}c^{12}=-5a^{11}b^{21}c^{12}\).

Ответ: 1) \(45a^{10}b^2\); 2) \(-8x^{30}y^{26}\); 3) \(a^4b^3c^{14}\); 4) \(\frac15m^7n^3p^{18}\); 5) \(\frac23a^8b^{10}\); 6) \(-5a^{11}b^{21}c^{12}\).