Question

Find the value of $\left\{\left(\frac{-3}{5}\right)^{-3}\right\}^2$.

• A. $\left(\frac{3}{5}\right)^6$
• B. $\left(\frac{5}{3}\right)^6$
• C. $\left(\frac{-3}{5}\right)^6$
• D. None

Answer 1

Answer: (B)

$\left\{\left(\frac{-3}{5}\right)^{-3}\right\}^2 $
$ =\left(\frac{-3}{5}\right)^{-6}=\left(\frac{-5}{3}\right)^6$
$ =(-1)^6\left(\frac{5}{3}\right)^6=\left(\frac{5}{3}\right)^6$
$\begin{Bmatrix}\because\left(\frac{a^m}{b}\right)^n=\left(\frac{a}{b}\right)^{m n} \\(-1)^6=1 \\a^{-m}=\frac{1}{a^m}\end{Bmatrix}$