Find the product of \[\left( a+\frac{1}{a} \right)\left( {{a}^{2}}+\frac{1}{{{a}^{2}}} \right)\left( {{a}^{4}}+\frac{1}{{{a}^{4}}} \right)\left( {{a}^{8}}+\frac{1}{{{a}^{8}}} \right)\left( a-\frac{1}{a} \right)\]

• A. \[{{a}^{16}}+\frac{1}{{{a}^{16}}}\]
• B.       \[{{a}^{16}}-\frac{1}{{{a}^{16}}}\]
• C. \[{{a}^{16}}+\frac{1}{{{a}^{16}}}+\frac{3}{8}{{a}^{8}}+\frac{1}{4{{a}^{8}}}\]          
• D. \[{{a}^{16}}+\frac{1}{{{a}^{16}}}+\frac{3}{8}{{a}^{8}}-\frac{1}{8{{a}^{8}}}\]
• E. None of these