Q. Simpllify
e) ${\left(\frac{1}{2}\right)}^{-2}+{\left(\frac{1}{3}\right)}^{-2}+{\left(\frac{1}{4}\right)}^{-2}$

Please find below the solution to the asked query:

We have : ${\left(\frac{1}{2}\right)}^{-2} +{\left(\frac{1}{3}\right)}^{-2} + {\left(\frac{1}{4}\right)}^{-2}$

$$\begin{gathered} \mathrm{We} \mathrm{know} : {\mathrm{a}}^{-\mathrm{m}} = \frac{1}{{\mathrm{a}}^{\mathrm{m}}} , \mathrm{So} \\ \Rightarrow {\left(\frac{1}{{\displaystyle \frac{1}{2}}}\right)}^2 +{\left(\frac{1}{{\displaystyle \frac{1}{3}}}\right)}^2 + {\left(\frac{1}{{\displaystyle \frac{1}{4}}}\right)}^2 \\ \Rightarrow {\left(2\right)}^2 +{\left(3\right)}^2 + {\left(4\right)}^2 \\ \Rightarrow 4 +9+16 \\ \mathbf{\Rightarrow }\mathbf{29}\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{(}\mathbf{ }\mathbf{Ans}\mathbf{ }\mathbf{)} \end{gathered}$$

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