To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80] and the first few multiples of 12 are [12, 24, 36, 48, 60, 72, 84, 96]. The first few multiples they share are [24, 48, 72, 96] making 24 the smallest multiple 8 and 12 share.

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

\( \frac{6 x 3}{8 x 3} \) + \( \frac{3 x 2}{12 x 2} \)

\( \frac{18}{24} \) + \( \frac{6}{24} \)

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

\( \frac{18 + 6}{24} \) = \( \frac{24}{24} \) = 1

The equation for this sequence is:

a_n = a_n-1 + 8

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 + 8
a₆ = 33 + 8
a₆ = 41

The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [30, 60, 90] making 30 the smallest multiple 6 and 10 have in common.

If 74% of the town's 41,000 voters cast ballots the number of votes cast is:

(\( \frac{74}{100} \)) x 41,000 = \( \frac{3,034,000}{100} \) = 30,340

The mayor got 90% of the votes cast which is:

(\( \frac{90}{100} \)) x 30,340 = \( \frac{2,730,600}{100} \) = 27,306 votes.

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