Question

Find the reciprocal of the answer​

Answer 1

—› Your Answer:

$\implies \rm \: \frac{( - { \frac{3}{2} )}^{ - 1} \times { (\frac{2}{3}) }^{2} }{( { \frac{2}{3}) }^{ - 1} \div ( \frac{3}{2} )}$

We know that, When the power is negative, we reciprocal the number to make a positive.

$\implies \rm \: \frac{( - { \frac{2}{3} )}^{1} \times ( { \frac{2}{3} )}^{2} }{( { \frac{3}{2} )}^{1} \div ( \frac{3}{2} )}$

$\implies \rm \: \frac{ - \frac{2}{3} \times \frac{4}{3} }{ \frac{3}{2} \times \frac{2}{3} }$

$\implies \rm \: \frac{ - \frac{8}{9} }{ \frac{ \cancel3}{ \cancel2} \times \frac{ \cancel2}{ \cancel3} }$

$\implies \rm \: \frac{ - \frac{ 8}{9} }{1} = - \frac{8}{9}$

So, since we have to find the reciprocal of answer,

$\implies \rm \: \frac{9}{8 } \: ..ans$