To raise a term with an exponent to another exponent, retain the base and multiply the exponents:

First, solve for \( \left|a + 7\right| \):

\( \left|a + 7\right| \) - 8 = 2
\( \left|a + 7\right| \) = 2 + 8
\( \left|a + 7\right| \) = 10

The value inside the absolute value brackets can be either positive or negative so (a + 7) must equal + 10 or -10 for \( \left|a + 7\right| \) to equal 10:

So, a = -17 or a = 3.

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 6 workers at the company now and that's enough to staff 3 crews so there are \( \frac{6}{3} \) = 2 workers on a crew. 6 crews are needed for the busy season which, at 2 workers per crew, means that the roofing company will need 6 x 2 = 12 total workers to staff the crews during the busy season. The company already employs 6 workers so they need to add 12 - 6 = 6 new staff for the busy season.

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

-5z⁷ x 3z⁷
(-5 x 3)z^{(7 + 7)}
-15z¹⁴

The equation for this sequence is:

a_n = a_n-1 + 2(n - 1)

where n is the term's order in the sequence, a_n is the value of the term, and a_n-1 is the value of the term before a_n. This makes the next number:

a₆ = a₅ + 2(6 - 1)
a₆ = 21 + 2(5)
a₆ = 31