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

To calculate this, we first need to convert the mixed number 3 2/7 to an improper fraction:

3 2/7 = (3 * 7 + 2)/7 = 23/7

Now we can raise it to the 8th power:

(23/7)^8 = (23^8)/(7^8) = 7942800461/5764801

Next, we calculate (7/23)^6:

(7/23)^6 = (7^6)/(23^6) = 117649/148035889

Now we multiply these two fractions:

(7942800461/5764801) (117649/148035889)
= (7942800461 117649) / (5764801 * 148035889)
= 935404435089389/854668640289

Therefore, (3 2/7)^8 * (7/23)^6 = 935404435089389/854668640289.