To square the expression (3/5a^5b - 2/3a^3b^4), we will distribute and simplify using the formula (a - b)^2 = a^2 - 2ab + b^2.

(3/5a^5b - 2/3a^3b^4)^2
= ((3/5a^5b)^2 - 2(3/5a^5b)(2/3a^3b^4) + (2/3a^3b^4)^2)
= ((9/25)(a^10)(b^2) - (4/5)(a^8)(b^5) + (4/9)(a^6)(b^8))
= (9/25)a^10b^2 - (4/5)a^8b^5 + (4/9)a^6b^8

Therefore, the square of the expression (3/5a^5b - 2/3a^3b^4) is (9/25)a^10b^2 - (4/5)a^8b^5 + (4/9)a^6b^8.