If 2\(^{a}\) = \(\sqrt{64}\) and \(\frac{b}{a}\) = 3, evaluate a\(^2 + b^{2}\)
A
250
B
160
C
90
D
48
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
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
Source: Myschool Past Questions Archive (Record #57238)