Question

Simplify :

$\text{(a)}{\left(\frac{2}{3}\right)}^{-3}\times {\left(\frac{2}{3}\right)}^{-1}\text{(b)}{\left[{\left(\frac{-1}{2}\right)}^{-3}\right]}^{-2}$

Answer 1

(a) The given product can be written as-

${\left(\frac{2}{3}\right)}^{-3}\times {\left(\frac{2}{3}\right)}^{-1}={\left(\frac{2}{3}\right)}^{-3+(-1)}={\left(\frac{2}{3}\right)}^{-4}={\left(\frac{3}{2}\right)}^4=\frac{81}{18}$

$\text{(b) The exponent}{\left[{\left(\frac{-1}{2}\right)}^{-3}\right]}^{-2}\text{can be written as}{\left(\frac{-1}{2}\right)}^{\left[\right(-3)\times (-2\left)\right]}={\left(\frac{-1}{2}\right)}^6=\frac{1}{64}$