Question

Find the multiplicative inverse of:-
$\boxed{ \sf \left( \: \dfrac{3}{5} \: \right) ^{ - 3} \div \left( \: \dfrac{5}{3} \: \right) ^{5} }$
​

Answer 1

Question

${ \sf \: Multiplicative \ inverse\ of: \sf \left( \: \dfrac{3}{5} \: \right) ^{ - 3} \div \left( \: \dfrac{5}{3} \: \right) ^{5} }$

$\sf \: Answer= \dfrac{25}{9}$

Step by step explanation

1) Method

${ \implies \sf \left( \: \dfrac{3}{5} \: \right) ^{ - 3} \div \left( \: \dfrac{5}{3} \: \right) ^{5} }$

${ \implies \sf \left( \: \dfrac{5}{3} \: \right) ^{ 3} \div \left( \: \dfrac{5}{3} \: \right) ^{5} }$

${ \implies \sf \left( \: \dfrac{5}{3} \: \right) ^{ 3 - 5} }$

${ \implies \sf \left( \: \dfrac{5}{3} \: \right) ^{ - 2} }$

${ \implies \sf \left( \: \dfrac{3}{5} \: \right) ^{ 2} }$

${ ~~~~~ \sf \left( \: \dfrac{9}{25} \: \right) }$

$\sf \: Now \: Multiplicative \: inverse \: of: \dfrac{9}{25} =\pink{ \dfrac{25}{9}}$

2) Method

${ \implies \sf \left( \: \dfrac{3}{5} \: \right) ^{ - 3} \div \left( \: \dfrac{5}{3} \: \right) ^{5} }$

${ \implies \sf \left( \: \dfrac{5}{3} \: \right) ^{ 3} \div \left( \: \dfrac{5}{3} \: \right) ^{5} }$

${ \implies \sf \left( \: \dfrac{5}{3} \: \right) ^{ 3} \times \left( \: \dfrac{3}{5} \: \right) ^{5} }$

${ \implies \sf \dfrac{125}{27} \times \dfrac{243}{3125} }$

${ \implies \sf \dfrac{\cancel{125¹}}{\cancel{27}¹} \times \dfrac{\cancel{243}⁹}{\cancel{3125}²⁵} }$

${\implies \sf \dfrac{9}{27} }$

$\sf \: Now \: Multiplicative \: inverse \: of: \dfrac{9}{25} = \pink{ \dfrac{25}{9}}$

Answer 2

Step-by-step explanation:

multiplicative inverse= 25/9