Answer:
[tex]\boxed {-\frac{12}{5}}[/tex]
Step-by-step explanation:
Solve the following expression:
[tex](-\frac{2}{3})^{7} \times (\frac{3}{5})^{6} \times (\frac{5}{6})^{5} \times (\frac{1}{3})^{-7}[/tex]
-Calculate [tex]-\frac{2}{3}[/tex] to the power of [tex]7[/tex]:
[tex](-\frac{2}{3})^{7} \times (\frac{3}{5})^{6} \times (\frac{5}{6})^{5} \times (\frac{1}{3})^{-7}[/tex]
[tex]-\frac{128}{2187} \times (\frac{3}{5})^{6} \times (\frac{5}{6})^{5} \times (\frac{1}{3})^{-7}[/tex]
-Calculate [tex]\frac{3}{5}[/tex] to the power of [tex]6[/tex]:
[tex]-\frac{128}{2187} \times (\frac{3}{5})^{6} \times (\frac{5}{6})^{5} \times (\frac{1}{3})^{-7}[/tex]
[tex]-\frac{128}{2187} \times (\frac{729}{15625}) \times (\frac{5}{6})^{5} \times (\frac{1}{3})^{-7}[/tex]
-Multiply both [tex]-\frac{128}{2187}[/tex] and [tex]\frac{729}{15625}[/tex]:
[tex]-\frac{128}{2187} \times (\frac{729}{15625}) \times (\frac{5}{6})^{5} \times (\frac{1}{3})^{-7}[/tex]
[tex]-\frac{128}{46875} \times (\frac{5}{6})^{5} \times (\frac{1}{3})^{-7}[/tex]
-Calculate [tex]\frac{5}{6}[/tex] to the power of [tex]5[/tex]:
[tex]-\frac{128}{46875} \times (\frac{5}{6})^{5} \times (\frac{1}{3})^{-7}[/tex]
[tex]-\frac{128}{46875} \times (\frac{3125}{7776}) \times (\frac{1}{3})^{-7}[/tex]
-Multiply both [tex]-\frac{128}{46875}[/tex] and [tex]\frac{3125}{7776}[/tex]:
[tex]-\frac{128}{46875} \times (\frac{3125}{7776}) \times (\frac{1}{3})^{-7}[/tex]
[tex]-\frac{4}{3645} \times (\frac{1}{3})^{-7}[/tex]
-Calculate [tex]\frac{1}{3}[/tex] to the power of [tex]-7[/tex]:
[tex]-\frac{4}{3645} \times (\frac{1}{3})^{-7}[/tex]
[tex]-\frac{4}{3645} \times 2181[/tex]
-Multiply both the [tex]-\frac{4}{3645}[/tex] and [tex]2187[/tex]:
[tex]-\frac{4}{3645} \times 2181[/tex]
[tex]\boxed {-\frac{12}{5}}[/tex]
Therefore, the final answer is [tex]-\frac{12}{5}[/tex].
