the value of (a^1/8 +a^-1/8) (a^1/8-a^1/8) (a^1/4+a^-1/4) (a^1/2 + a ^-1/2)
is equal to

Dear Student, Your question must be : (a^{\frac{1}{8}} + a^{\frac{- 1}{8}}) (a^{\frac{1}{8}} - a^{\frac{- 1}{8}}) (a^{\frac{1}{4}} + a^{\frac{- 1}{4}}) (a^{\frac{1}{2}} + a^{\frac{- 1}{2}}) = (a^{\frac{1}{4}} - a^{\frac{- 1}{4}}) (a^{\frac{1}{4}} + a^{\frac{- 1}{4}}) (a^{\frac{1}{2}} + a^{\frac{- 1}{2}}) [Since (a^{\frac{1}{8}} + a^{\frac{- 1}{8}}) (a^{\frac{1}{8}} - a^{\frac{- 1}{8}}) = ({(a^{\frac{1}{8}})}^{2} - {(a^{\frac{- 1}{8}})}^{2} = (a^{\frac{1}{4}} - a^{\frac{- 1}{4}}))] = (a^{\frac{1}{2}} - a^{\frac{- 1}{2}}) (a^{\frac{1}{2}} + a^{\frac{- 1}{2}}) = ({(a^{\frac{1}{2}})}^{2} - {(a^{\frac{- 1}{2}})}^{2}) = a - a^{- 1} = a - \frac{1}{a} Regards