## To simplify the expression (-2x^2y)^3*(5xy^3)^2, we need to apply the rules of exponents.

First, let's simplify (-2x^2y)^3. To raise a power to a power, we multiply the exponents. So, (-2x^2y)^3 becomes (-2^3)(x^2)^3(y)^3, which simplifies to -8x^6y^3.

Next, we simplify (5xy^3)^2. Again, applying the rule of exponents, we get (5^2)(x)^2(y^3)^2, which further simplifies to 25x^2y^6.

Now, we multiply the two simplified expressions together: (-8x^6y^3)*(25x^2y^6). By multiplying the coefficients and combining the variables, we get -200x^8y^9.

So, the simplified expression is -200x^8y^9.