(3 2/7)^8 * (7/23)^6

First, we need to convert the mixed number 3 2/7 to an improper fraction:
3 2/7 = 23/7

Now, let's simplify the expression:

(23/7)^8 (7/23)^6
= (23^8 / 7^8) (7^6 / 23^6)
= (79235168 / 5764801) (117649 / 887503681)
= 0.344454 0.000133
= 0.000045862

Therefore, (3 2/7)^8 * (7/23)^6 is approximately equal to 0.000045862.