Answer
(a) $(-\frac{3}{5})^{3}=(-\frac{3}{5})\times(-\frac{3}{5})\times(-\frac{3}{5})=-\frac{27}{125}$
(b) $(\frac{3^{2}}{2})^{-3}=(\frac{9}{2})^{-3}=(\frac{2}{9})^3=\frac{2}{9}\times\frac{2}{9}\times\frac{2}{9}=\frac{8}{729}$
(c) $\frac{5^{3} 7^{-1}}{5^{2} 7}=\frac{5^{3}}{5^{2}}\times\frac{7^{-1}}{7}=5^{3-2}\times7^{-1-1}=5^{1}\times 7^{-2}=\frac{5}{7^{2}}=\frac{5}{49}$
(d)$(2^{3})^{-2}=(2\times2\times2)^{-2}=(8)^{-2}=(\frac{1}{8})^{2}=\frac{1}{64}$
Work Step by Step
(a) $(-\frac{3}{5})^{3}=(-\frac{3}{5})\times(-\frac{3}{5})\times(-\frac{3}{5})=-\frac{27}{125}$
(b) $(\frac{3^{2}}{2})^{-3}=(\frac{9}{2})^{-3}=(\frac{2}{9})^3=\frac{2}{9}\times\frac{2}{9}\times\frac{2}{9}=\frac{8}{729}$
(c)$\frac{5^{3} 7^{-1}}{5^{2} 7}=\frac{5^{3}}{5^{2}}\times\frac{7^{-1}}{7}=5^{3-2}\times7^{-1-1}=5^{1}\times 7^{-2}=\frac{5}{7^{2}}=\frac{5}{49}$
(d)$(2^{3})^{-2}=(2\times2\times2)^{-2}=(8)^{-2}=(\frac{1}{8})^{2}=\frac{1}{64}$
