Question

Simplify : ( 8/27 )−2/3 × (4 / 9)−3 /2 and write the result in positive exponential form.

Answer 1

Step-by-step explanation:

$( { \frac{8}{27}) }^{ - \frac{ 2}{3} } \times ( { \frac{4}{9} )}^{ - \frac{3}{2} } \\ \\ = ({ (\frac{2}{3} )}^{3} ) {}^{ - \frac{2}{3} } \times (({ \frac{2}{3} )}^{2} ) {}^{ - \frac{3}{2} } \\ \\ = ({ \frac{2}{3} )}^{3 \times ( - \frac{2}{3} )} \times {( \frac{2}{3} )}^{2 \times ( - \frac{3}{2}) } \\ \\ = ( { \frac{2}{3} )}^{ - 2} \times ({ \frac{2}{3} )}^{ - 3} \\ \\ = \frac{1}{ ({ \frac{2}{3}) }^{2} } \times \frac{1}{ ({ \frac{2}{3} })^{3} } \\ \\ = (\frac{3}{2} ) {}^{2} \times( { \frac{3}{2} )}^{3} \\ \\ = ({ \frac{3}{2} )}^{2 + 3} \\ \\ = ( { \frac{3}{2}) }^{5} \\ \\ \\ using \: \: formula \: \: (({x}) {}^{m} ) {}^{n } = {x}^{ m\times \: n } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: {x}^{ - n} = \frac{1}{ {x}^{n} } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: {x}^{m} \times {x}^{n} = {x}^{ m+ n}$