Question

Evaluate : ${\left(27\right)}^{-1/3}\times (27{)}^{-1/3}\times [{27}^{1/3}-{27}^{2/3}]$

Answer 1

${\left(27\right)}^{-1/3}\times [{27}^{1/3}-{27}^{2/3}]$
$={\left(3^3\right)}^{-1/3}\times [{3^3}^{1/3}-{3^3}^{2/3}]$
$={\left(3\right)}^{-3/3}\times [3^{3/3}-3^{2\times 3/3}]$
$=3^{-1}\times [3-3^2]$
$=\frac{1}{3}\times [3-9]$
$=\frac{1}{3}\times [-6]$
$=-2$