Question

(-2/3)^7*(3/5)^6*(5/6)^5*(1/3)^-7 simplify of law of indices ​

Answer 1

Answer:

$\boxed {-\frac{12}{5}}$

Step-by-step explanation:

Solve the following expression:

$(-\frac{2}{3})^{7} \times (\frac{3}{5})^{6} \times (\frac{5}{6})^{5} \times (\frac{1}{3})^{-7}$

-Calculate $-\frac{2}{3}$ to the power of $7$:

$(-\frac{2}{3})^{7} \times (\frac{3}{5})^{6} \times (\frac{5}{6})^{5} \times (\frac{1}{3})^{-7}$

$-\frac{128}{2187} \times (\frac{3}{5})^{6} \times (\frac{5}{6})^{5} \times (\frac{1}{3})^{-7}$

-Calculate $\frac{3}{5}$ to the power of $6$:

$-\frac{128}{2187} \times (\frac{3}{5})^{6} \times (\frac{5}{6})^{5} \times (\frac{1}{3})^{-7}$

$-\frac{128}{2187} \times (\frac{729}{15625}) \times (\frac{5}{6})^{5} \times (\frac{1}{3})^{-7}$

-Multiply both $-\frac{128}{2187}$ and $\frac{729}{15625}$:

$-\frac{128}{2187} \times (\frac{729}{15625}) \times (\frac{5}{6})^{5} \times (\frac{1}{3})^{-7}$

$-\frac{128}{46875} \times (\frac{5}{6})^{5} \times (\frac{1}{3})^{-7}$

-Calculate $\frac{5}{6}$ to the power of $5$:

$-\frac{128}{46875} \times (\frac{5}{6})^{5} \times (\frac{1}{3})^{-7}$

$-\frac{128}{46875} \times (\frac{3125}{7776}) \times (\frac{1}{3})^{-7}$

-Multiply both $-\frac{128}{46875}$ and $\frac{3125}{7776}$:

$-\frac{128}{46875} \times (\frac{3125}{7776}) \times (\frac{1}{3})^{-7}$

$-\frac{4}{3645} \times (\frac{1}{3})^{-7}$

-Calculate $\frac{1}{3}$ to the power of $-7$:

$-\frac{4}{3645} \times (\frac{1}{3})^{-7}$

$-\frac{4}{3645} \times 2181$

-Multiply both the $-\frac{4}{3645}$ and $2187$:

$-\frac{4}{3645} \times 2181$

$\boxed {-\frac{12}{5}}$

Therefore, the final answer is $-\frac{12}{5}$.