When simplified and written with positive exponents, the expression $(27 x)^{-\frac{2}{3}} \times(125 x)^{\frac{1}{3}}$ becomes

Step 1 ：First, we rewrite the expression using the properties of exponents: $(27 x)^{-\frac{2}{3}} \times(125 x)^{\frac{1}{3}} = 27^{-\frac{2}{3}} \times x^{-\frac{2}{3}} \times 125^{\frac{1}{3}} \times x^{\frac{1}{3}}$

Step 2 ：Next, we simplify the numerical parts and the variable parts separately: $27^{-\frac{2}{3}} \times 125^{\frac{1}{3}} = (3^3)^{-\frac{2}{3}} \times (5^3)^{\frac{1}{3}} = 3^{-2} \times 5 = \frac{1}{9} \times 5 = \frac{5}{9}$

Step 3 ：Then, we simplify the variable parts: $x^{-\frac{2}{3}} \times x^{\frac{1}{3}} = x^{-\frac{2}{3} + \frac{1}{3}} = x^{-\frac{1}{3}}$

Step 4 ：Finally, we combine the numerical part and the variable part to get the final answer: $\frac{5}{9} \times x^{-\frac{1}{3}} = \boxed{\frac{5}{9}x^{-\frac{1}{3}}}$