Question

by what number should (2/-3)‐³ be divided so that the quotient is (4/9)‐²?​

Answer 1

Step-by-step explanation:

${\implies{ (\frac{2}{ - 3} ) }^{ - 3} \div x = ({ \frac{4}{9} })^{ - 2} } \\ {\implies({ \frac{ - 3}{2} })^{ 3} \div x = ({ \frac{9}{4} })^{2} } \\{\implies {x = ( \frac{9}{4} ) {}^{2} \times ( \frac{ - 3}{2} ) {}^{3} }} \\ {\implies{x = \frac{81}{16} \times \frac{ - 27}{8} }} \\{\implies{ x = \frac{2187}{128} }} \\ {\implies{x = \frac{ ({3})^{7} }{ ({2})^{7} } }} \\ {\boxed{\implies{x = ({\frac{3}{7} }) ^{7} }}}$