1: \(75^3:\left(-25\right)^3=\left(\dfrac{75}{-25}\right)^3=\left(-3\right)^3=-27\)
2: \(\left(-60\right)^2:\left(-5\right)^2=\dfrac{60^2}{5^2}=12^2=144\)
3: \(169^2:\left(-13\right)^2=\dfrac{169^2}{13^2}=\left(\dfrac{169}{13}\right)^2=13^2=169\)
4: \(\left(\dfrac{1}{2}\right)^2:\left(\dfrac{3}{2}\right)^2=\left(\dfrac{1}{2}:\dfrac{3}{2}\right)^2=\left(\dfrac{1}{3}\right)^2=\dfrac{1}{9}\)
5: \(\left(\dfrac{2}{3}\right)^3:\left(\dfrac{8}{27}\right)^3=\left(\dfrac{2}{3}:\dfrac{8}{27}\right)^3=\left(\dfrac{2}{3}\cdot\dfrac{27}{8}\right)^3=\left(\dfrac{9}{4}\right)^3=\dfrac{729}{64}\)
6: \(\left(\dfrac{5}{4}\right)^4:\left(\dfrac{15}{2}\right)^4=\left(\dfrac{5}{4}:\dfrac{15}{2}\right)^4=\left(\dfrac{5}{4}\cdot\dfrac{2}{15}\right)^4=\left(\dfrac{1}{6}\right)^4=\dfrac{1}{1296}\)
7: \(\left(\dfrac{7}{8}\right)^5:\left(\dfrac{21}{16}\right)^5\)
\(=\left(\dfrac{7}{8}:\dfrac{21}{16}\right)^5\)
\(=\left(\dfrac{7}{8}\cdot\dfrac{16}{21}\right)^5=\left(\dfrac{2}{3}\right)^5=\dfrac{32}{243}\)
8: \(\left(\dfrac{5}{6}\right)^4:\left(\dfrac{25}{18}\right)^4=\left(\dfrac{5}{6}:\dfrac{25}{18}\right)^4=\left(\dfrac{5}{6}\cdot\dfrac{18}{25}\right)^4=\left(\dfrac{3}{5}\right)^4=\dfrac{81}{625}\)
9:
\(\left(-\dfrac{3}{4}\right)^3:\left(\dfrac{9}{8}\right)^3=\left(-\dfrac{3}{4}:\dfrac{9}{8}\right)^3=\left(-\dfrac{3}{4}\cdot\dfrac{8}{9}\right)^3\)
\(=\left(-\dfrac{2}{3}\right)^3=-\dfrac{8}{27}\)
10:
\(\left(\dfrac{9}{10}\right)^6:\left(\dfrac{27}{-20}\right)^6=\left(\dfrac{9}{10}:\dfrac{-27}{20}\right)^6\)
\(=\left(\dfrac{9}{10}\cdot\dfrac{20}{-27}\right)^6=\left(-\dfrac{2}{3}\right)^6=\dfrac{64}{729}\)
