First, solve for \( \left|b + 8\right| \):

\( \left|b + 8\right| \) + 5 = -1
\( \left|b + 8\right| \) = -1 - 5
\( \left|b + 8\right| \) = -6

The value inside the absolute value brackets can be either positive or negative so (b + 8) must equal - 6 or --6 for \( \left|b + 8\right| \) to equal -6:

So, b = -2 or b = -14.

If 69% of the town's 39,000 voters cast ballots the number of votes cast is:

(\( \frac{69}{100} \)) x 39,000 = \( \frac{2,691,000}{100} \) = 26,910

The mayor got 66% of the votes cast which is:

(\( \frac{66}{100} \)) x 26,910 = \( \frac{1,776,060}{100} \) = 17,761 votes.

To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:

\( \sqrt{\frac{49}{36}} \)
\( \frac{\sqrt{49}}{\sqrt{36}} \)
\( \frac{\sqrt{7^2}}{\sqrt{6^2}} \)
\( \frac{7}{6} \)
1\(\frac{1}{6}\)

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:

-5b⁵ - 3b⁵
(-5 - 3)b⁵
-8b⁵

To simplify this fraction, first find the greatest common factor between them. The factors of 20 are [1, 2, 4, 5, 10, 20] and the factors of 60 are [1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60]. They share 6 factors [1, 2, 4, 5, 10, 20] making 20 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{20}{60} \) = \( \frac{\frac{20}{20}}{\frac{60}{20}} \) = \( \frac{1}{3} \)