There are 3 3-passenger taxis available so that's 3 x 3 = 9 total seats. There are 14 people needing transportation leaving 14 - 9 = 5 who will have to find other transportation.

First, solve for \( \left|a - 2\right| \):

\( \left|a - 2\right| \) + 9 = 2
\( \left|a - 2\right| \) = 2 - 9
\( \left|a - 2\right| \) = -7

The value inside the absolute value brackets can be either positive or negative so (a - 2) must equal - 7 or --7 for \( \left|a - 2\right| \) to equal -7:

So, a = 9 or a = -5.

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [10, 20, 30, 40, 50] making 10 the smallest multiple 2 and 10 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{4 x 5}{2 x 5} \) - \( \frac{8 x 1}{10 x 1} \)

\( \frac{20}{10} \) - \( \frac{8}{10} \)

Now, because the fractions share a common denominator, you can subtract them:

\( \frac{20 - 8}{10} \) = \( \frac{12}{10} \) = 1\(\frac{1}{5}\)

A number with an exponent (b^e) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b¹ = b) and a base with an exponent of 0 equals 1 ( (b⁰ = 1).

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so subtract the coefficients and retain the base and exponent:

-5z⁷ - 4z⁷
(-5 - 4)z⁷
-9z⁷