Question

Simplify 0.3 power 2/3 into 1/27 power 1/4 into 9 power 1/6 into 0.81 power 2/3 divided by 0.9 power 2/3 into 3 power -1/2 into 1/3 power -2 into 243 power -1/4

Answer 1

Using Laws of exponents, The above expression can be simplified as follows.

$= \large \frac{0.3 ^{ \frac{2}{3} } \times \frac{1}{ {27}^{ \frac{1}{4} } } \times {9}^{ \frac{1}{6} } \times {0.81}^{ \frac{2}{3} } }{ {0.9}^{ \frac{2}{3} } \times {3}^{ \frac{ - 1}{2} } \times \frac{1}{3 ^{ - 2} } \times {243}^{ \frac{ - 1 }{4} } } \\ \\ = \large \frac{\frac{1}{ {27}^{ \frac{1}{4} } } \times {9}^{ \frac{1}{6} } \times {0.81}^{ \frac{2}{3} } }{ {3}^{ \frac{ - 1}{2} } \times \frac{1}{3 ^{ - 2} } \times {243}^{ \frac{ - 1 }{4} } } \times ( \frac{0.3}{0.9} ) ^{ \frac{2}{3} } \\ \\ = \frac{ {3}^{ \frac{ - 3}{4} } \times {3}^{ \frac{2}{6} } \times {3}^{ \frac{2 \times 4}{3} } }{ {3}^{ \frac{ - 1}{2} } \times {3}^{2} \times {3}^{ \frac{ - 5}{4} } } \times (\frac{1}{3} ) ^{ \frac{2}{3} } \times {10}^{ \frac{ - 4}{3} } \\ \\ = 3 ^{ \frac{ - 3}{4} + \frac{1}{3} + \frac{8}{3} + \frac{1}{2} - 2 + \frac{5}{4} - \frac{2}{3} } \times {10}^{ \frac{ - 4}{3} } \\ \\ = {3}^{ \frac{5 - 3}{4} + \frac{1}{2} - 2 + \frac{7}{3} } \times {10}^{ \frac{ - 4}{3} } \\ \\ = {3}^{ - 1 + \frac{7}{3} } \times {10}^{ \frac{ - 4}{3} } \\ \\ = (3 \times 10) ^{ \frac{ - 4}{3} } \\ \\ = {30}^{ \frac{ - 4}{3} }$