SAT Exponents

Algebra Level 2

If \(a\) and \(b\) are positive non-consecutive integers and \(4^{a} \cdot 4^{b} = 1024\), which of the following equals \(2^{a} + 2^{b}?\)

(A) \(\ \ 5\)
(B) \(\ \ 12\)
(C) \(\ \ 18\)
(D) \(\ \ 32\)
(E) \(\ \ 1024\)

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