If 2(^{a}) = (sqrt{64}) and (frac{b}{a}) = 3, evaluate a(^2 + b^{2})

If 2\(^{a}\) = \(\sqrt{64}\) and \(\frac{b}{a}\) = 3, evaluate a\(^2 + b^{2}\)

The correct answer is: C

2\(^a\) = \(\sqrt{64}\)

2\(^a\) = 8

2\(^a\) = 2\(^3\)

a = 3

b = 3\(^a\)

b = 3 x 3 = 9

a\(^2\) + b\(^2\) = 3\(^2\) + 9\(^2\)

= 9 + 81 = 90