Question

Find the multiplicative inverse of (–7)^–2 ÷ (90)^–1.

Answer 1

As we know that a is called multiplicative inverse of b, If a × b = 1.

Given:

(–7)^–2 ÷ (90)^–1 

Simplify the above expression as follows:

${\displaystyle {(-7)}^{-2}÷{\left(90\right)}^{-1}=\frac{1}{{\left(7\right)}^2}÷\frac{1}{{\left(90\right)}^1}}$

= ${\displaystyle \frac{1}{49}÷\frac{1}{90}}$

= ${\displaystyle \frac{1}{49}\times \frac{90}{1}}$

= ${\displaystyle \frac{90}{49}}$ 

Let ${\displaystyle b=\frac{90}{49}}$

So, ${\displaystyle a\times \frac{90}{49}=1}$

${\displaystyle a=\frac{49}{90}}$

Hence, the multiplicative inverse is ${\displaystyle \frac{49}{90}}$.