1.

Solve it.Find the value of (1/2)^-2 + (1/3)^-2 + (1/2)^-2​

Answer» <html><body><p>We have given <img align="absmiddle" alt="\large{\bf{\green{(\frac{1}{2})^{-2} + (\frac{1}{3})^{-2} + (\frac{1}{4})^{-2}}}}" class="latex-formula" id="TexFormula1" src="https://tex.z-dn.net/?f=%5Clarge%7B%5Cbf%7B%5Cgreen%7B%28%5Cfrac%7B1%7D%7B2%7D%29%5E%7B-2%7D%20%2B%20%28%5Cfrac%7B1%7D%7B3%7D%29%5E%7B-2%7D%20%2B%20%28%5Cfrac%7B1%7D%7B4%7D%29%5E%7B-2%7D%7D%7D%7D" title="\large{\bf{\green{(\frac{1}{2})^{-2} + (\frac{1}{3})^{-2} + (\frac{1}{4})^{-2}}}}"/>. So to solve these type of questions, we <a href="https://interviewquestions.tuteehub.com/tag/required-1185621" style="font-weight:bold;" target="_blank" title="Click to know more about REQUIRED">REQUIRED</a> some formulas of <strong>Exponent</strong><strong>.</strong><strong> </strong>In this question, we will use a formula which says that <img align="absmiddle" alt="(\frac{1}{n})^{-m}" class="latex-formula" id="TexFormula2" src="https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7Bn%7D%29%5E%7B-m%7D" title="(\frac{1}{n})^{-m}"/> can be written as <img align="absmiddle" alt="{n}^{m}" class="latex-formula" id="TexFormula3" src="https://tex.z-dn.net/?f=%20%7Bn%7D%5E%7Bm%7D%20" title="{n}^{m}"/>. </p><h2>_______________________</h2><p><strong><u>Let's </u></strong><strong><u>understand</u></strong><strong><u> </u></strong><strong><u>that </u></strong><strong><u>what </u></strong><strong><u>does </u></strong><strong><u>this </u></strong><strong><u>formula</u></strong><strong><u> </u></strong><strong><u><a href="https://interviewquestions.tuteehub.com/tag/saying-629505" style="font-weight:bold;" target="_blank" title="Click to know more about SAYING">SAYING</a>:</u></strong></p><p>This formula says that, if <strong>power </strong>of any number is in negative form and if we will <strong>reverse </strong>the number, then the power became <strong>positive</strong><strong>.</strong><strong> </strong>Similarly, in this question also, we have given 3 <a href="https://interviewquestions.tuteehub.com/tag/numbers-22758" style="font-weight:bold;" target="_blank" title="Click to know more about NUMBERS">NUMBERS</a> (in fraction form) and powers are negative. So for solving further, we need to make power positive. <a href="https://interviewquestions.tuteehub.com/tag/using-7379753" style="font-weight:bold;" target="_blank" title="Click to know more about USING">USING</a> this formula (mentioned above), if we reverse the number then power became positive.</p><h2>_______________________</h2><p></p><p><strong><u>Considering</u></strong><strong><u> </u></strong><strong><u>above</u></strong><strong><u> </u></strong><strong><u>formula</u></strong><strong><u>:</u></strong></p><p></p><p><img align="absmiddle" alt="\large{\bf{(\frac{1}{2})^{-2} + (\frac{1}{3})^{-2} + (\frac{1}{4})^{-2}}}" class="latex-formula" id="TexFormula4" src="https://tex.z-dn.net/?f=%5Clarge%7B%5Cbf%7B%28%5Cfrac%7B1%7D%7B2%7D%29%5E%7B-2%7D%20%2B%20%28%5Cfrac%7B1%7D%7B3%7D%29%5E%7B-2%7D%20%2B%20%28%5Cfrac%7B1%7D%7B4%7D%29%5E%7B-2%7D%7D%7D" title="\large{\bf{(\frac{1}{2})^{-2} + (\frac{1}{3})^{-2} + (\frac{1}{4})^{-2}}}"/></p><p><img align="absmiddle" alt="\implies\large{\bf{2^2+3^2+4^2}}" class="latex-formula" id="TexFormula5" src="https://tex.z-dn.net/?f=%5Cimplies%5Clarge%7B%5Cbf%7B2%5E2%2B3%5E2%2B4%5E2%7D%7D" title="\implies\large{\bf{2^2+3^2+4^2}}"/></p><p><img align="absmiddle" alt="\implies\large{\bf{4+9+16}}" class="latex-formula" id="TexFormula6" src="https://tex.z-dn.net/?f=%5Cimplies%5Clarge%7B%5Cbf%7B4%2B9%2B16%7D%7D" title="\implies\large{\bf{4+9+16}}"/></p><p><img align="absmiddle" alt="\implies\large{\bf{13+16}}" class="latex-formula" id="TexFormula7" src="https://tex.z-dn.net/?f=%5Cimplies%5Clarge%7B%5Cbf%7B13%2B16%7D%7D" title="\implies\large{\bf{13+16}}"/></p><p><img align="absmiddle" alt="\implies\large{\bf{29}}" class="latex-formula" id="TexFormula8" src="https://tex.z-dn.net/?f=%5Cimplies%5Clarge%7B%5Cbf%7B29%7D%7D" title="\implies\large{\bf{29}}"/></p><h2>_______________________</h2><p></p><h3><u><a href="https://interviewquestions.tuteehub.com/tag/know-534065" style="font-weight:bold;" target="_blank" title="Click to know more about KNOW">KNOW</a></u><u> </u><u>more </u><u>formulas</u><u> </u><u>related</u><u> </u><u>to </u><u>this </u><u>type </u><u>of</u><u> questions</u><u>:</u></h3><p></p><ul><li><img align="absmiddle" alt="\large{\sf{(\frac{a}{b})^m\times(\frac{a}{b})^n~=~(\frac{a}{b})^{m+n}}}" class="latex-formula" id="TexFormula9" src="https://tex.z-dn.net/?f=%5Clarge%7B%5Csf%7B%28%5Cfrac%7Ba%7D%7Bb%7D%29%5Em%5Ctimes%28%5Cfrac%7Ba%7D%7Bb%7D%29%5En~%3D~%28%5Cfrac%7Ba%7D%7Bb%7D%29%5E%7Bm%2Bn%7D%7D%7D" title="\large{\sf{(\frac{a}{b})^m\times(\frac{a}{b})^n~=~(\frac{a}{b})^{m+n}}}"/> </li><li><img align="absmiddle" alt="\large{\sf{\bigg[(\frac{a}{b})^m\bigg]^n~=~(\frac{a}{b})^{mn}}}" class="latex-formula" id="TexFormula10" src="https://tex.z-dn.net/?f=%5Clarge%7B%5Csf%7B%5Cbigg%5B%28%5Cfrac%7Ba%7D%7Bb%7D%29%5Em%5Cbigg%5D%5En~%3D~%28%5Cfrac%7Ba%7D%7Bb%7D%29%5E%7Bmn%7D%7D%7D" title="\large{\sf{\bigg[(\frac{a}{b})^m\bigg]^n~=~(\frac{a}{b})^{mn}}}"/></li><li><img align="absmiddle" alt="\large{\sf{(\frac{a}{b})^m\times(\frac{c}{d})^m~=~\bigg({\frac{a}{b}\times {\frac{c}{d}\bigg)^m}}}}" class="latex-formula" id="TexFormula11" src="https://tex.z-dn.net/?f=%5Clarge%7B%5Csf%7B%28%5Cfrac%7Ba%7D%7Bb%7D%29%5Em%5Ctimes%28%5Cfrac%7Bc%7D%7Bd%7D%29%5Em~%3D~%5Cbigg%28%7B%5Cfrac%7Ba%7D%7Bb%7D%5Ctimes%20%7B%5Cfrac%7Bc%7D%7Bd%7D%5Cbigg%29%5Em%7D%7D%7D%7D" title="\large{\sf{(\frac{a}{b})^m\times(\frac{c}{d})^m~=~\bigg({\frac{a}{b}\times {\frac{c}{d}\bigg)^m}}}}"/> </li><li><img align="absmiddle" alt="\large{\sf{(\frac{a}{b})^m\div (\frac{a}{b})^n~=~(\frac{a}{b})^{m-n}}}" class="latex-formula" id="TexFormula12" src="https://tex.z-dn.net/?f=%5Clarge%7B%5Csf%7B%28%5Cfrac%7Ba%7D%7Bb%7D%29%5Em%5Cdiv%20%28%5Cfrac%7Ba%7D%7Bb%7D%29%5En~%3D~%28%5Cfrac%7Ba%7D%7Bb%7D%29%5E%7Bm-n%7D%7D%7D" title="\large{\sf{(\frac{a}{b})^m\div (\frac{a}{b})^n~=~(\frac{a}{b})^{m-n}}}"/></li></ul></body></html>


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