117. Возведите в степень: а) \(\left(\frac{x}{2y}\right)^3\); б) \(\left(\frac{3a}{c}\right)^4\); в) \(\left(\frac{n^2}{10m}\right)^3\); г) \(\left(\frac{9a^3}{2b^2}\right)^2\).

Используем правило \(\left(\frac{u}{v}\right)^n=\frac{u^n}{v^n}\).

1. \[\left(\frac{x}{2y}\right)^3=\frac{x^3}{8y^3}.\]
2. \[\left(\frac{3a}{c}\right)^4=\frac{81a^4}{c^4}.\]
3. \[\left(\frac{n^2}{10m}\right)^3=\frac{n^6}{1000m^3}.\]
4. \[\left(\frac{9a^3}{2b^2}\right)^2=\frac{81a^6}{4b^4}.\]

Ответ: а) \(\frac{x^3}{8y^3}\); б) \(\frac{81a^4}{c^4}\); в) \(\frac{n^6}{1000m^3}\); г) \(\frac{81a^6}{4b^4}\).