Question

Simplify
$\left(\frac{1}{27}\right)\times 2^{-3}$

Answer 1

$\left(\frac{1}{27}\right)\times 2^{-3}$
$27$ can be expressed as $3\times 3\times 3=3^3$
So, $\left(\frac{1}{27}\right)\times 2^{-3}=\frac{1}{3^3}\times 2^{-3}$
$=\frac{1}{3^3}\times \frac{1}{2^3}$ $(\because a^{-m}=\frac{1}{a^m})$
$=\frac{1}{{(3\times 2)}^3}$ ($\because a^m\times b^m={\left(ab\right)}^m$)
$=\frac{1}{6^3}=\frac{1}{216}$