1. 5√6 * 1/6√216

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

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

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.

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.

Thanks!

To solve the first expression, 5√6 * 1/6√216, follow these steps:

Step 1: Simplify the square roots.
√6 can't be simplified further, but √216 can.
√216 = √36 * √6 = 6√6

So the expression becomes 5√6 * 1/6√6

Step 2: Simplify the fractions.
To simplify 1/6√6, multiply both the numerator and denominator by √6.
(1 * √6) / (6√6 * √6) = √6 / 6 * 6 = √6 / 36

The expression is now 5√6 * √6 / 36

Step 3: Multiply the constants and variables separately.
5 * √6 * √6 = 5 * 6 = 30
The variables cancel out since there are no variables present.

So the simplified expression is 30 / 36

Step 4: Simplify the fraction.
Both 30 and 36 can be divided by 6.
30 / 6 = 5 and 36 / 6 = 6.

Therefore, the final answer is 5/6.

Now let's solve the second expression, -9√28a^2 * 1/3√63a.

Step 1: Simplify the square roots.
√28 can be simplified further to 2√7.
√63 can be simplified further to 3√7.

So the expression becomes -9 * 2√7a^2 * 1 / 3 * 3√7a

Step 2: Simplify the fractions.
To simplify 1/3√7a, multiply both the numerator and denominator by √7a.
(1 * √7a) / (3√7a * √7a) = √7a / 3 * 7a = √7a / 21a^2

The expression is now -9 * 2√7a^2 / √7a / 21a^2

Step 3: Multiply the constants and variables separately.
-9 * 2 = -18

So the expression becomes -18√7a^2 / √7a / 21a^2

Step 4: Simplify the square roots.
The square roots cancel out since there are both a square root and its inverse present.
-18 * 1 / 21a^2 = -18 / 21a^2

Step 5: Simplify the fraction.
-18 and 21 both have a common factor of 3.
-18 / 21 = -6 / 7.

Therefore, the final answer is -6 / 7a^2.