Ответ:

  1. \((3m^7n^5)^2=3^2m^{14}n^{10}=9m^{14}n^{10}\).
  2. \((-2x^3y)^3=-8x^9y^3\).
  3. \((-5a^4b^2c^3)^2=25a^8b^4c^6\).
  4. \(\left(-\frac13ab^5\right)^4=\frac1{81}a^4b^{20}\).
  5. \((13x^5y^6z^7)^2=169x^{10}y^{12}z^{14}\).
  6. \(2\frac13=\frac73\), поэтому \(\left(\frac73m^{24}n^{18}\right)^3=\frac{343}{27}m^{72}n^{54}\).

Ответ: 1) \(9m^{14}n^{10}\); 2) \(-8x^9y^3\); 3) \(25a^8b^4c^6\); 4) \(\frac1{81}a^4b^{20}\); 5) \(169x^{10}y^{12}z^{14}\); 6) \(\frac{343}{27}m^{72}n^{54}\).