question_answer

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