Question

find the value of 4 √81 ki power -2

Answer 1

$\pink{ \boxed{ \bf4\sqrt{(81)}^{-2} = \dfrac{1}{9}}}$

Method 1

$\\ \sf\: \: \: \: \: \: \: \: \: \implies4\sqrt{(81)}^{-2}$

$\sf\: \: \: \: \: \: \: \: \: \implies4\sqrt{( {3}^{4} )}^{-2}$

$\sf\: \: \: \: \: \: \: \: \: \implies3^{-2}$

$\sf\: \: \: \: \: \: \: \: \: \implies \dfrac{1}{ {3}^{2} }$

$\sf\: \: \: \: \: \: \: \: \: \implies \dfrac{1}{ 9 }$

Method 2

$\\ \sf\: \: \: \: \: \: \: \: \: \implies4\sqrt{(81)}^{-2}$

$\sf\: \: \: \: \: \: \: \: \: \implies( {3}^{4} )^{-2 \times \frac{1}{4}}$

$\sf\: \: \: \: \: \: \: \: \: \implies( {3} )^{ 4\times \frac{ - 1}{2}}$

$\sf\: \: \: \: \: \: \: \: \: \implies {3}^{ - 2}$

$\bf\: \: \: \: \: \: \: \: \: \implies \dfrac{1}{9}$

• $\tiny\begin{gathered}\begin{gathered}\\\\\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered} \bigstar \: \underline{\bf{}}\\ {\boxed{\begin{array}{c | c} \frac{ \: ~~~~~~~~~~\: \: \: \: \:\sf Laws \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }{ } &\frac{ \: ~~~~~~~~~~ \: \: \: \: \:\sf Example \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }{ }\\ \sf \bigstar{a}^{m} \times {a}^{n} = {a}^{m + n} & \sf {a}^{2} \times {a}^{3} = {a}^{2 + 3} = {a}^{6} \\ \\ \sf \bigstar{a}^{m} \div {a}^{n} = {a}^{m - n}& \sf {a}^{3} \div {a}^{2} = {a}^{3 - 2} = {a}^{1} \\ \\ \sf{\bigstar \: \: \: \: \: \: ( {a}^{m} ) ^{n} = {a}^{mn} } & \sf( {a}^{2} ) ^{3} = {a}^{2 \times 3} = {a}^{6} \\ \\ {\bigstar\sf a {}^{m} \times {n}^{m} = (ab) ^{m} } &\sf a {}^{2} \times {b}^{2} = (ab) ^{2}\\ \\ \sf\bigstar \: \: \: \: \: {a}^{0} = 1& \sf {2}^{0} = 1 \: \: \: \: \\ \\ \sf \bigstar \: \: \: \: {\dfrac{ {a}^{m} }{ {b}^{m} }= \left( \dfrac{a}{b} \right) ^{m} }& \sf{\dfrac{ {a}^{2} }{ {b}^{2} }= \left( \dfrac{a}{b} \right) ^{2} }\\\\\bigstar~~~~~~~ \sf x^{\frac{m}{n} }=\sqrt[n]{x^m}\sf = (\sqrt[n]{x})^m & \sf x^{\frac{2}{3} }=\sqrt[3]{x^2} = (\sqrt[n]{x})^m\\ \\\\ \end{array}}}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}$

Answer 2

Answer:

See the attachment photos.

= 1/9.

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