Find the values of each of the following:
(i) $ \left(\frac{1}{2}\right)^{-1}+\left(\frac{1}{3}\right)^{-1}+\left(\frac{1}{4}\right)^{-1} $
(ii) $ \left(\frac{1}{2}\right)^{-2}+\left(\frac{1}{3}\right)^{-2}+\left(\frac{1}{4}\right)^{-2} $
(iii) $ \left(2^{-1} \times 4^{-1}\right) \div 2^{-2} $
(iv) $ \left(5^{-1} \times 2^{-1}\right) \div 6^{-1} $

To do:  

We have to find the values of each of the given expressions.

Solution:

We know that,

$a^{-m}=\frac{1}{a^{m}}$

Therefore,

(i) $(\frac{1}{2})^{-1}+(\frac{1}{3})^{-1}+(\frac{1}{4})^{-1}=(2)^{1}+(3)^{1}+(4)^{1}$

$=2+3+4$

$=9$

(ii) $(\frac{1}{2})^{-2}+(\frac{1}{3})^{-2}+(\frac{1}{4})^{-2}=(2)^{2}+(3)^{2}+(4)^{2}$

$=4+9+16$

$=29$

(iii) $(2^{-1} \times 4^{-1}) \div 2^{-2}=(\frac{1}{2} \times \frac{1}{4}) \div \frac{1}{2^{2}}$

$=\frac{1}{8} \div \frac{1}{4}$

$=\frac{1}{8} \times \frac{4}{1}$

$=\frac{1}{2}$

(iv) $(5^{-1} \times 2^{-1}) \div 6^{-1}=(\frac{1}{5} \times \frac{1}{2}) \div \frac{1}{6}$

$=\frac{1}{10} \times \frac{6}{1}$

$=\frac{6}{10}$

$=\frac{3}{5}$

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Updated on: 10-Oct-2022

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