Question

Find the value of the expression
${\left[3^{1/3}{\{5^{-1/2}\times 3^{-1/3}\times ({225}^2{)}^{1/3}\}}^{-1/2}\right]}^6$

Answer 1

Solution:

${\left[3^{1/3}\right\{5^{-1/2}\times 3^{-1/3}\times \left({225}^2{)}^{1/3}{\}}^{-1/2}\right]}^6$

$={\left[3^{1/3}\right\{5^{-1/2}\times 3^{-1/3}\times \left(15{)}^{4/3}{\}}^{-1/2}\right]}^6$

$={\left[3^{1/3}\right\{5^{-1/2}\times 3^{-1/3}\times 5^{4/3}\times 3^{4/3}{\}}^{-1/2}]}^6$

$={\left[3^{1/3}\right\{5^{5/6}\times 3{\}}^{-1/2}]}^6$

$={[3^{1/3}\times 5^{-5/12}\times 3^{-1/2}]}^6$

$={[3^{-1/6}\times 5^{-5/12}]}^6$

$=3^{-1}\times 5^{-5/2}$