A ratio of 3:1 means that there are 3 home fans for every one visiting fan. So, of every 4 fans, 3 are home fans and \( \frac{3}{4} \) of every fan in the stadium is a home fan:

49,000 fans x \( \frac{3}{4} \) = \( \frac{147000}{4} \) = 36,750 fans.

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 11 are [11, 22, 33, 44, 55, 66, 77, 88, 99]. The first few multiples they share are [33, 66, 99] making 33 the smallest multiple 3 and 11 share.

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

\( \frac{5 x 11}{3 x 11} \) + \( \frac{7 x 3}{11 x 3} \)

\( \frac{55}{33} \) + \( \frac{21}{33} \)

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

\( \frac{55 + 21}{33} \) = \( \frac{76}{33} \) = 2\(\frac{10}{33}\)

If 64% of the town's 25,000 voters cast ballots the number of votes cast is:

(\( \frac{64}{100} \)) x 25,000 = \( \frac{1,600,000}{100} \) = 16,000

The mayor got 68% of the votes cast which is:

(\( \frac{68}{100} \)) x 16,000 = \( \frac{1,088,000}{100} \) = 10,880 votes.

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.

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