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Exponents and Powers — MATHS STD 8 — Question

Gujarat BoardEnglish MediumSTD 8MATHSExponents and Powers2 Marks
Question
Evaluate.
(i) $\left\{\left(\frac{1}{3}\right)^{-1}-\left(\frac{1}{4}\right)^{-1}\right\}^{-1}$
(ii) $\left(\frac{5}{8}\right)^{-7} \times\left(\frac{8}{5}\right)^{-4}$
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Answer

(i)
We have, $\left\{\left(\frac{1}{3}\right)^{-1}-\left(\frac{1}{4}\right)^{-1}\right\}^{-1}$
$
\begin{array}{ll}
=\left\{\frac{(1)^{-1}}{(3)^{-1}}-\frac{(1)^{-1}}{(4)^{-1}}\right\}^{-1} \qquad {\left[\because\left(\frac{a}{b}\right)^m=\frac{a^m}{b^m}\right]} \\
=\left\{\frac{3}{1}-\frac{4}{1}\right\}^{-1} \qquad {\left[\because a^{-m}=\frac{1}{a^m}\right]} \\
=(3-4)^{-1}=(-1)^{-1}=\frac{1}{(-1)^1}\qquad \left[\because a^{-m}=\frac{1}{a^m}\right] \\
=\frac{1}{-1}=-1
\end{array}
$
(ii) Ans. $\frac{512}{125}$

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