The expression for which the value has to be found can be simplified as follows:

\(\frac{4^{(a + b)}}{2^{(a - b)}}\) \(= \frac{2^{2(a + b)}}{2^{(a - b)}}\) \(= \frac{2^{2a + 2b)}}{2^{(a - b)}}\) = \(2^{2a + 2b - a + b} = 2^{a + 3b}\)

(1) a = 7

Just knowing the value of a,

we cannot find the value of the expression(Insufficient)

(2) a + 3b = 5

Since we have simplified the expression as \(2^{a + 3b}\)

knowing the value of\(a + 3b\) is enough

to find the value of the expression (Sufficient) (Option B)

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