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)

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