Question

The multiplicative inverse of ${\left(\frac{-5}{9}\right)}^{-99}$is?

• A. ${\left(\frac{-5}{9}\right)}^{99}$
• B. ${\left(\frac{5}{9}\right)}^{99}$
• C. ${\left(\frac{9}{-5}\right)}^{99}$
• D. ${\left(\frac{9}{5}\right)}^{99}$

Answer 1

The correct option is A

${\left(\frac{-5}{9}\right)}^{99}$

Use the definition of multiplicative inverse

For any two real numbers $a.$ and $b$ if their product $a\times b=1$

Then $b$ is the multiplicative inverse of $a.$and vice versa.

Let $x$ be the multiplicative inverse of ${\left(\frac{-5}{9}\right)}^{-99}$

$$\begin{gathered} x\times {\left(\frac{-5}{9}\right)}^{-99}=1 \\ x=\frac{1}{{\left(\frac{-5}{9}\right)}^{-99}} \\ x={\left(\frac{-5}{9}\right)}^{99}\left[\because {\left(\frac{a}{b}\right)}^{-m}={\left(\frac{b}{a}\right)}^m\right] \end{gathered}$$

Thus, the multiplicative inverse of ${\left(\frac{-5}{9}\right)}^{-99}$ is ${\left(\frac{-5}{9}\right)}^{99}$

Hence, the correct option is A.