Question

Question 11

In the following question, out of the four options, only one is correct. Write the correct answer:

The multiplicative inverse of ${(-\frac{5}{9})}^{-99}$ is:
(a) ${(-\frac{5}{9})}^{99}$
(b) ${\left(\frac{5}{9}\right)}^{99}$
(c) ${(-\frac{9}{-5})}^{99}$
(d) ${(-\frac{9}{5})}^{99}$

Answer 1

For multiplicative inverse, a is called multiplicative inverse fo b, if $a\times b=1$
$\Rightarrow a\times {\left(\frac{-5}{9}\right)}^{-99}=1\Rightarrow a=\frac{1}{{\left(\frac{-5}{9}\right)}^{-99}}\Rightarrow a={\left(\frac{-5}{9}\right)}^{99}$