Question

The multiplicative inverse of ${\left(\frac{1}{2}\right)}^4÷{\left(\frac{1}{3}\right)}^4+{\left(-\frac{1}{3}\right)}^3$

Answer 1

Solution :- given

$={\left(\frac{1}{2}\right)}^4÷{\left(\frac{1}{3}\right)}^4+{\left(\frac{-1}{3}\right)}^3$

$\Rightarrow \frac{1}{2^4}÷\frac{1}{3^4}+{\left(\frac{-1}{3}\right)}^3$

$\Rightarrow \frac{1}{2^4}\times \frac{3^4}{1}+{\left(\frac{-1}{3}\right)}^3$

$\Rightarrow \frac{3^4}{2^4}-\frac{1}{3^3}$

$\Rightarrow \frac{81}{16}-\frac{1}{27}$

$\Rightarrow \frac{2187-16}{432}$

$\Rightarrow \frac{2171}{432}$

$\therefore$ Multiplicative inverse is $=\frac{432}{2171}$ (Ans)