I just want to make sure I have done this correctly.

yep.

Thank you.

To confirm if you have simplified the expression correctly, let's go through the steps together.

1. Start with the given expression: (10a^3b)(3ab^2c^2).
2. Multiply the coefficients: 10 * 3 = 30.
3. Multiply the "a" terms: a^3 * a = a^(3+1) = a^4.
4. Multiply the "b" terms: b * b^2 = b^(1+2) = b^3.
5. Multiply the "c" terms: There is only one "c" in the second expression, so it remains as c^2.
6. Put all the simplified terms together: 30a^4b^3c^2.

Based on these steps, it looks like you have simplified the expression correctly. Well done!