To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:

\( \frac{-4b^8}{9b^3} \)
\( \frac{-4}{9} \) b^{(8 - 3)}
-\(\frac{4}{9}\)b⁵

In order to find how many additional workers are needed to staff the extra crews you first need to calculate how many workers are on a crew. There are 9 workers at the company now and that's enough to staff 3 crews so there are \( \frac{9}{3} \) = 3 workers on a crew. 7 crews are needed for the busy season which, at 3 workers per crew, means that the roofing company will need 7 x 3 = 21 total workers to staff the crews during the busy season. The company already employs 9 workers so they need to add 21 - 9 = 12 new staff for the busy season.

To add these radicals together their radicands must be the same:

3\( \sqrt{28} \) + 8\( \sqrt{7} \)
3\( \sqrt{4 \times 7} \) + 8\( \sqrt{7} \)
3\( \sqrt{2^2 \times 7} \) + 8\( \sqrt{7} \)
(3)(2)\( \sqrt{7} \) + 8\( \sqrt{7} \)
6\( \sqrt{7} \) + 8\( \sqrt{7} \)

Now that the radicands are identical, you can add them together:

The factors of 28 are [1, 2, 4, 7, 14, 28] and the factors of 80 are [1, 2, 4, 5, 8, 10, 16, 20, 40, 80]. They share 3 factors [1, 2, 4] making 4 the greatest factor 28 and 80 have in common.

The commutative property states that, when adding or multiplying numbers, the order in which they're added or multiplied does not matter. For example, 3 + 4 and 4 + 3 give the same result, as do 3 x 4 and 4 x 3.