Gujarat BoardEnglish MediumSTD 8MATHSExponents and Powers2 Marks
Question
Find the multiplicative inverse of $(-7)^{-2}÷ (90)^{-1}$.
✓
Answer
a is called multiplicative inverse of b, if $a \times b = 1$
We have, $(-7)^{-2}÷ (90)^{-1}$
$=\frac{1}{(7)^2}+\frac{1}{(90)^1}$
$=\frac{1}{49}\div\frac{1}{90}$
$=\frac{1}{49}\times\frac{90}{1}$
$=\frac{90}{49}$
$\Big[\because$ $(-a)^m= a^m$ if $m$ is an even number and $\text{a}^{-\text{m}}=\frac{1}{\text{a}^\text{m}}\Big]$
Put $\text{b}=\frac{90}{49}$
$\therefore$ $\text{a}\times\frac{90}{49}=1$
$\Rightarrow\text{a}\times\frac{90}{49}$
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