Question

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

• A. $9$
• B. $\frac{1}{9}$
• C. $\frac{1}{4}$
• D. None of these

Answer 1

The correct option is B $\frac{1}{9}$

Given rational number is ${\left(\frac{1}{3}\right)}^{-2}$

To find out,

The multiplicative inverse of the given rational number.

Let the multiplicate inverse be $x$.

We know that, the multiplicative inverse of a number is another number which when multiplied by the original number yields $1$ as a product.

We also know that, ${\left(\frac{a}{b}\right)}^{-m}={\left(\frac{b}{a}\right)}^m$

$\therefore {\left(\frac{1}{3}\right)}^{-2}=3^2$

$=9$

Now, $9\times x=1$

$\therefore x=\frac{1}{9}$

Hence, the multiplicative inverse of ${\left(\frac{1}{3}\right)}^{-2}$ is $\frac{1}{9}$.