Question

Simplify:${\left(\frac{1}{2}\right)}^3\times {\left(\frac{-3}{2}\right)}^3\times {\left(\frac{3}{2}\right)}^3$

Answer 1

${\left(\frac{1}{2}\right)}^3\times {\left(\frac{-3}{2}\right)}^3\times {\left(\frac{3}{2}\right)}^3$

$=\frac{{(-3)}^3\times 3^3}{2^3\times 2^3\times 2^3}$ [Since, $(\frac{a}{b}{)}^m=\frac{a^m}{b^m},b\ne 0$]

$=\frac{-27\times 27}{8\times 8\times 8}$

$=\frac{-729}{512}$

$\therefore {\left(\frac{1}{2}\right)}^3\times {\left(\frac{-3}{2}\right)}^3\times {\left(\frac{3}{2}\right)}^3=\frac{-729}{512}$