Question

(8*2_10)_2*3 to the 7th power = 4374

Answer 1

I think you mean

(8 * 2^10)^2 * 3^7
(2^13)^2 * 3^7
2^26 * 3^7
67108864 * 2187
146767085568

Clearly I have misinterpreted your unusual syntax.