A) \[{{5}^{2/3}}+1+{{5}^{-2/3}}\]
B) \[{{5}^{1/3}}-{{5}^{-1/3}}\]
C) \[{{5}^{2/3}}-1+{{5}^{-2/3}}\]
D) \[{{5}^{2/3}}+1-{{5}^{-2/3}}\]
Correct Answer: C
Solution :
\[{{5}^{\frac{1}{3}}}+{{5}^{\frac{-1}{3}}}\]is in the form of \[(a+b)\]. We know that \[(a+b)({{a}^{2}}-ab+{{b}^{2}})={{a}^{3}}+{{b}^{3}}.\] So, the simplest R.F. of \[{{5}^{\frac{1}{3}}}+{{5}^{\frac{-1}{3}}}\]is \[{{\left( {{5}^{\frac{1}{3}}} \right)}^{2}}-\left( {{5}^{\frac{1}{3}}} \right)\left( {{5}^{\frac{-1}{3}}} \right)+{{\left( {{5}^{\frac{-1}{3}}} \right)}^{2}}\] \[={{5}^{\frac{2}{3}}}-1+{{5}^{\frac{-2}{3}}}\]
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