\[\begin{eqnarray}X&=&a^1\cdot b^3 \cdot c^5\cdot \cdot \cdot \cdot z^{51} \\ Y&=&z^1 \cdot y^3 \cdot x^5 \cdot \cdot \cdot \cdot a^{51} \end{eqnarray}\]

If \(a \cdot b \cdot c \cdot d \cdot \cdot \cdot \cdot z=(-24389)^{\frac{1}{156}}\), then find the value of \(XY\).

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