$\text{ Let }{A}_1,A_2,A_3,\dots \dots A_{11}\text{ be }11\text{ Arithmetic means and }{H}_1,H_2,H_3,\dots .H_{11}\text{ be }11\text{ Harmonic means and }{G}_1,G_2,G_3,\dots \dots G_{11}\text{ be }11\text{ Geometric means }$

$\text{ between two numbers }1\text{ and }9\text{ then value of }\prod _{k=1}^5 \left(A_k\cdot G_{12-2k}\cdot H_{12-k}\right)\text{ is }$