Simplify the following:
(9)52−3.(5)0−(181)−12(9)^{\dfrac{5}{2}} - 3.(5)^0 - \Big(\dfrac{1}{81}\Big)^{-\dfrac{1}{2}}(9)25−3.(5)0−(811)−21
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Given,
⇒(32)52−3.1−(192)−12=32×52−3−(92)12=35−3−9=243−12=231.\Rightarrow (3^2)^{\dfrac{5}{2}} - 3.1 - \Big(\dfrac{1}{9^2}\Big)^{-\dfrac{1}{2}} \\[1em] = 3^{2 \times \dfrac{5}{2}} - 3 - (9^2)^{\dfrac{1}{2}} \\[1em] = 3^5 - 3 - 9 \\[1em] = 243 - 12 \\[1em] = 231.⇒(32)25−3.1−(921)−21=32×25−3−(92)21=35−3−9=243−12=231.
Hence, (9)52−3.(5)0−(181)−12(9)^{\dfrac{5}{2}} - 3.(5)^0 - \Big(\dfrac{1}{81}\Big)^{-\dfrac{1}{2}}(9)25−3.(5)0−(811)−21 = 231.
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