Question

Evaluate

1. {$(\frac{1}{3})^{−1} − (\frac{1}{4})^{−1}$}−1
2. $(\frac{5}{8})^{−7}× (\frac{8}{5})^{−4}$

Answer 1

(i) {$(\frac{1}{3})^{−1} − (\frac{1}{4})^{−1}$}−1

$(\frac{a}{b})^{−m} = (\frac{b}{a})^m$

{$(\frac{1}{3})^{−1} − (\frac{1}{4})^{−1}$}−1
$= (3^1 − 4^1)−1$
$= (3 − 4)^{−1}$
$= (−1)^{−1}$
$= (\frac{−1}{1})^1= −1$

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(ii) $(\frac{5}{8})^{−7}× (\frac{8}{5})^{−4}$

We know that, $(\frac{a}{b})^{−m} = (\frac{b}{a})^m$

$(\frac{5}{8})^{−7}× (\frac{8}{5})^{−4}$

$= (\frac{8}{5})^7 × (\frac{8}{5})^{−4}$

$= (\frac{8}{5})^3$ [Since, $\frac{a^m}{a^n} = a^{m - n}$]

$= \frac{512}{125}$