`@` `\text {Ans}`
`\downarrow`
\(3^2\cdot\dfrac{1}{243}\cdot81^2\cdot\dfrac{1}{3^3}\)
`=`\(\dfrac{3^2}{243}\cdot\dfrac{81^2}{3^3}\)
`=`\(\dfrac{3^2}{3^5}\cdot\dfrac{3^8}{3^3}=\dfrac{1}{3^3}\cdot3^5=\dfrac{3^5}{3^3}=3^2=9\)
\(3^2\cdot\dfrac{1}{243}\cdot81^2\cdot\dfrac{1}{3^2}\)
\(=3^2\cdot\dfrac{1}{3^5}\cdot\left(3^4\right)^2\cdot\dfrac{1}{3^2}\)
\(=3^2\cdot\dfrac{1}{3^5}\cdot3^8\cdot\dfrac{1}{3^2}\)
\(=\dfrac{3^2}{3^5}\cdot\dfrac{3^8}{3^2}\)
\(=\dfrac{3^2}{3^5}\cdot3^6\)
\(=\dfrac{3^2\cdot3^6}{3^5}\)
\(=3^2\cdot3\)
\(=3^3\)
\(=27\)
\(=\dfrac{3^2.81^2}{243.3^3}=\dfrac{3^2.3^4}{3^5.3^3}=\dfrac{3^6}{3^8}=\dfrac{1}{3^2}=\dfrac{1}{9}\)
\(3^2\times\dfrac{1}{243}\times81^2\times\dfrac{1}{3^3}\)
\(=\dfrac{3^2\times81^2}{243\times3^3}\)
\(=\dfrac{3^2\times\left(3^4\right)^2}{243\times3^3}\)
\(=\dfrac{3^2\times3^8}{3^5\times3^3}\)
\(=\dfrac{3^{2+8}}{3^{5+3}}\)
\(=\dfrac{3^{10}}{3^8}\)
\(=3^2\)
\(9\)
