1) \(\left(\dfrac{1}{2}\right)^3\cdot\left(\dfrac{3}{2}\right)^2=\dfrac{1}{8}\cdot\dfrac{9}{4}=\dfrac{9}{32}\)
2) \(\left(\dfrac{2}{3}\right)^3\cdot\left(\dfrac{3}{2}\right)^2=\dfrac{8}{27}\cdot\dfrac{9}{4}=\dfrac{1}{3}\cdot2=\dfrac{2}{3}\)
3) \(\left(\dfrac{3}{4}\right)^4\cdot\left(\dfrac{4}{3}\right)^5=\dfrac{81}{256}\cdot\dfrac{1024}{243}=\dfrac{4}{3}\)
4) \(\left(\dfrac{5}{4}\right)^5\cdot\left(\dfrac{4}{5}\right)^7=\dfrac{5^5\cdot4^7}{4^5\cdot5^7}=\dfrac{4^2}{5^2}=\dfrac{16}{25}\)
5) \(\left(-\dfrac{5}{6}\right)^6\cdot\left(\dfrac{6}{5}\right)^8=\dfrac{5^6\cdot6^8}{6^6\cdot5^8}=\dfrac{6^2}{5^2}=\dfrac{36}{25}\)
6) \(\left(\dfrac{1}{2}\right)^3\cdot\left(-\dfrac{4}{7}\right)^3=-\dfrac{1\cdot2^6}{2^3\cdot7^3}=\dfrac{-8}{343}\)
7) \(\left(-\dfrac{4}{3}\right)^3\cdot\left(\dfrac{9}{16}\right)^5=-\dfrac{4^3}{3^3}\cdot\dfrac{3^{10}}{4^{10}}=\dfrac{-3^7}{4^7}=-\dfrac{2187}{16384}\)
8) \(\left(\dfrac{1}{3}\right)^4\cdot\left(-\dfrac{9}{2}\right)^6=\dfrac{1\cdot3^{12}}{3^4\cdot2^6}=\dfrac{3^8}{2^6}=\dfrac{6561}{64}\)
9) \(\left(-\dfrac{13}{8}\right)^3\cdot\left(-\dfrac{32}{13}\right)^4=-\dfrac{13^3\cdot2^{20}}{2^9\cdot13^4}=\dfrac{2^{11}}{13}=\dfrac{2048}{13}\)
