Terms want Freedom

Algebra Level 5

Given pp and qq are positive real numbers that satisfy the equation p4+q3=2p^4 + q^3 = 2 . What is the maximum value of the term independent of xx in the expansion below?

(p x112+q x19)14 \large \left ( p \space x^{\frac {1}{12}} + q \space x^{-\frac {1}{9}} \right )^{14}

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