Question

Simplify (9^1\3×27^-1\3)\(3^1\6×3^-2\3)

Answer 1

Solution :

$\frac{ {9}^{ \frac{1}{3} } \times {27}^{ - \frac{1}{3} }}{ {3}^{ \frac{1}{6}} \times {3}^{ - \frac{2}{3} } } \\ \\ = \frac{ ({{3}^{2 }) }^{ \frac{1}{3} } \times { ({3}^{3} )}^{ - \frac{ 1}{3} } }{ {3}^{ \frac{1}{6} + \frac{ - 2}{3} } } = \frac{ {3}^{ \frac{2}{3} } \times {3}^{ - \frac{ 3}{3} } }{ {3}^{ \frac{1 - 4}{6} } } \\ \\ = \frac{ {3}^{ \frac{2}{3} + \frac{ - 3}{3} } }{ {3}^{ \frac{ - 3}{6} } } = \frac{ {3}^{ \frac{2 - 3}{3} } }{ {3}^{ \frac{ - 1}{2} } } = \frac{ {3}^{ \frac{ - 1}{3} } }{ {3}^{ \frac{ - 1}{2} } } \\ \\ = {3}^{ \frac{ - 1}{3} - \frac{ - 1}{2} } = {3}^{ \frac{ - 2 - ( - 3)}{6} } = {3}^{ \frac{ - 2 + 3}{6} } \\ \\ = {3}^{ \frac{1}{6} } \: \: \: \: \: \: \: \textbf{Ans.}$