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To simplify this expression, we need to use the rules of exponents. First, we can simplify the numerator and denominator separately by using the quotient rule:
(3x^3y^2z^6/xy^-2z^3) = 3x^(3-1)y^(2+2)z^(6-3) = 3x^2y^4z^3
Now, we can plug this simplified expression into our original expression:
(3x^3y^2z^6/xy^-2z^3)^2 = (3x^2y^4z^3)^2
To simplify this expression further, we can use the power rule:
(3x^2y^4z^3)^2 = 3^2 x^(2*2) y^(4*2) z^(3*2) = 9x^4y^8z^6
Therefore, the simplified expression is 9x^4y^8z^6.