Question

Find the multiplicative inverse of $(-7{)}^{-2}÷(90{)}^{-1}$.

Answer 1

$a$ is called multiplactive inverse of $b$, if $a\times b=1$
We have ,$(-7{)}^{-2}÷(90{)}^{-1}=\frac{1}{(7{)}^2}÷\frac{1}{{90}^1}=\frac{1}{49}÷\frac{1}{90}=\frac{1}{49}\times \frac{90}{1}=\frac{90}{49}.$
Let us take,
$b=\frac{90}{49}\therefore a\times \frac{90}{49}=1\Rightarrow a=\frac{49}{90}$