1. 5√6 * 1/6√216

Question

5/6 * √1296
5/6 * √144 * √9
= 30

2. -9√28a^2 * 1/3√63a

-3√1764a^3
-3√49a^2 * √36a
-3*7a*6√a
= -126a√a

Answer 1

5√6 * 1/(6√216)
5√6 * 1/(6*6√6)
5/36

If you meant

-9√(28a^2) * 1/(3√(63a))
-9(2a√7) * 1/(3*3√(7a))
-18a√7 / 9√7√a
= -2√a

Answer 2

The problems are 5√6 * (1/6)√216 and -9√28a^2 * (1/3)√63a.

Actually, I checked my final answers, but I just wanted to make sure that my process is correct.

Answer 3

In that case, you are correct.

The expressions are complicated enough that if you came up with the correct answers, your process was likely correct.

Answer 4

Thanks!