Evaluate the following :
(32−5)13(32+5)13(\sqrt{32}-\sqrt{5})^{\dfrac{1}{3}} (\sqrt{32}+\sqrt{5})^{\dfrac{1}{3}}(32−5)31(32+5)31
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Given,
Simplifying the expression :
⇒[(32−5)(32+5)]13⇒[(32)2−(5)2]13⇒[32−5]13⇒[27]13⇒(33)13⇒3.\Rightarrow [(\sqrt{32}-\sqrt{5})(\sqrt{32}+\sqrt{5})]^{\dfrac{1}{3}} \\[1em] \Rightarrow [(\sqrt{32})^2-(\sqrt{5})^2]^{\dfrac{1}{3}} \\[1em] \Rightarrow [32 - 5]^{\dfrac{1}{3}} \\[1em] \Rightarrow [27]^{\dfrac{1}{3}} \\[1em] \Rightarrow (3^3)^{\dfrac{1}{3}} \\[1em] \Rightarrow 3.⇒[(32−5)(32+5)]31⇒[(32)2−(5)2]31⇒[32−5]31⇒[27]31⇒(33)31⇒3.
Hence, (32−5)13 (32+5)13=3(\sqrt{32}-\sqrt{5})^{\dfrac{1}{3}} \ (\sqrt{32}+\sqrt{5})^{\dfrac{1}{3}} = 3(32−5)31 (32+5)31=3.
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(27)43+(32)0.8+(0.8)−1+(0.8)0(27)^{\dfrac{4}{3}} + (32)^{0.8} + (0.8)^{-1} + (0.8)^0(27)34+(32)0.8+(0.8)−1+(0.8)0
[(27)−39−3]13\Big[\dfrac{(27)^{-3}}{9^{-3}}\Big]^{\dfrac{1}{3}}[9−3(27)−3]31
(9)52−3×(4)0−(181)−12(9)^{\dfrac{5}{2}} - 3 \times (4)^0 - \Big(\dfrac{1}{81}\Big)^{-\dfrac{1}{2}}(9)25−3×(4)0−(811)−21
Simplify :
3n×9n+13n−1×9n−1\dfrac{3^n \times 9^{n + 1}}{3^{n - 1} \times 9^{n - 1}}3n−1×9n−13n×9n+1
