(b) \(\frac{64}{729}.\)
(a2 + b2)3 = (a3+b3)2
⇒ a6 + b6 + 3a2b2 (a2 + b2) = a6 + b6 + 2a2b2
⇒ a2 + b2 = \(\frac23\) ab .....(i)
Now, \(\big(\frac{a}{b}+\frac{b}{a}\big)^6\) = \(\big(\frac{a^2+b^2}{ab}\big)^6\) = \(\bigg(\frac{\frac23ab}{ab}\bigg)^6\)= \(\big(\frac23\big)^6\) = \(\frac{64}{729}.\)