Evaluate i 1-3-1-1-4-1-1 ii 5-8-7-8-5-4

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Evaluate i 1/...

Question

Evaluate (i) ${(\frac{1}{3})^{- 1} - (\frac{1}{4})^{- 1}}^{- 1}$ (ii) $(\frac{5}{8})^{- 7} \times (\frac{8}{5})^{- 4}$

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Solution

(i) ${(\frac{1}{3})^{- 1} - (\frac{1}{4})^{- 1}}^{- 1}$
$= {(\frac{3}{1})^{1} - (\frac{4}{1})^{1}}^{- 1}$ [ $∵ (\frac{a}{b})^{- m} = (\frac{b}{a})^{m}$ ]
$= {3 - 4}^{- 1} = (- 1)^{- 1} = \frac{1}{- 1} = - 1$
(ii) $(\frac{5}{8})^{- 7} \times (\frac{8}{5})^{- 4}$
$= (\frac{5^{- 7}}{8^{- 7}}) \times (\frac{8^{- 4}}{5^{- 4}})$ [ $∵ {\frac{a}{b}}^{m} = \frac{a^{m}}{b^{m}}$ ]
$= \frac{8^{7}}{5^{7}} \times \frac{5^{4}}{8^{4}}$ [ $∵ a^{- m} = \frac{1}{a^{m}}$ ]
$= \frac{8^{7 - 4}}{5^{7 - 4}}$ [ $∵ a^{m} \div a^{n} = a^{m - n}$ ]
$= \frac{8^{3}}{5^{3}} = \frac{512}{125}$

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Evaluate (i) {(13)−1−(14)−1}−1 (ii) (58)−7×(85)−4

(i) {(13)−1−(14)−1}−1={(31)1−(41)1}−1 [∵(ab)−m=(ba)m]={3−4}−1=(−1)−1=1−1=−1(ii) (58)−7×(85)−4=(5−78−7)×(8−45−4) [∵{ab}m=ambm]=8757×5484 [∵a−m=1am]=87−457−4 [∵am÷an=am−n]=8353=512125

Evaluate (i) ${(\frac{1}{3})^{- 1} - (\frac{1}{4})^{- 1}}^{- 1}$ (ii) $(\frac{5}{8})^{- 7} \times (\frac{8}{5})^{- 4}$