Question

9 raise to power 1 upon 3 into 27 raised to power 1/2 upon 3 raised to power 1/6 × 3 raised to power -2/3

Answer 1

Given expression =${9}^{ \frac{1}{3} } \times \frac{ {27}^{ \frac{1}{2} } }{ {3}^{ \frac{1}{6} } } \times {3}^{ \frac{ - 2}{3} }$
=${3}^{ \frac{2}{3} } \times \frac{ {3}^{ \frac{3}{2} } }{ {3}^{ \frac{1}{6} } } \times \frac{1}{ {3}^{ \frac{2}{3} } }$

=${3}^{ \frac{2}{3} + \frac{3}{2} - \frac{1}{6} - \frac{2}{3} }$
=${3}^{ \frac{4 + 9 - 1 - 4}{6} }$
=${3}^{ \frac{8}{6} }$
=${3}^{ \frac{4}{3} }$
=${81}^{ \frac{1}{3} }$
=3√3

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Answer 2

{9}^{ \frac{1}{3} } \times \frac{ {27}^{ \frac{1}{2} } }{ {3}^{ \frac{1}{6} } } \times {3}^{ \frac{ - 2}{3} }
= {3}^{ \frac{2}{3} } \times \frac{ {3}^{ \frac{3}{2} } }{ {3}^{ \frac{1}{6} } } \times \frac{1}{ {3}^{ \frac{2}{3} } }

= {3}^{ \frac{2}{3} + \frac{3}{2} - \frac{1}{6} - \frac{2}{3} }
= {3}^{ \frac{4 + 9 - 1 - 4}{6} }
= {3}^{ \frac{8}{6} }
= {3}^{ \frac{4}{3} }
= {81}^{ \frac{1}{3} }
=3√3

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