Exponential Recap II

Algebra Level 2

\[\begin{cases} \large 2^{x+y}\cdot 4^x=64 \\ \large 16^{x+y}\cdot 2^{-y}=16\end{cases} \]

Solve the system for \(x\) and \(y\). If \(x+y\) is equal to \(\dfrac ab\), where \(a\) and \(b\) are coprime positive integers, submit your answer as \(a+b\).

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