1. The problem is to simplify the expression involving powers of $x$: $$x^{-2} \times x^{-5} \times x^{3} \times x^{-3} \times x^{10} \times x^{7}.$$\n\n2. Recall the rule for multiplying powers with the same base: $$x^{a} \times x^{b} = x^{a+b}.$$\n\n3. Apply this rule by adding all the exponents: $$-2 + (-5) + 3 + (-3) + 10 + 7.$$\n\n4. Calculate the sum step-by-step: $$-2 - 5 = -7,$$\n$$-7 + 3 = -4,$$\n$$-4 - 3 = -7,$$\n$$-7 + 10 = 3,$$\n$$3 + 7 = 10.$$\n\n5. So the expression simplifies to: $$x^{10}.$$\n\n6. Final answer: $$\boxed{x^{10}}.$$