A point \(P\) inside a regular tetrahedron is such that its distance from all vertices \(A, B, C\) & \(D\) of the tetrahedron is the same. The line \(AP\), when produced, intersects the plane formed by vertices \(B, C\) & \(D\) at the point \(Q\). The ratio \(\frac{AP}{AQ}\) can be written as \(\frac{a}{b}\).
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Find \(a^{b}\).

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