The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90]. The first few multiples they share are [9, 18, 27, 36, 45] making 9 the smallest multiple 3 and 9 have in common.

If 44% of the town's 15,000 voters cast ballots the number of votes cast is:

(\( \frac{44}{100} \)) x 15,000 = \( \frac{660,000}{100} \) = 6,600

The mayor got 77% of the votes cast which is:

(\( \frac{77}{100} \)) x 6,600 = \( \frac{508,200}{100} \) = 5,082 votes.

To multiply terms with radicals, multiply the coefficients and radicands separately:

4\( \sqrt{2} \) x 8\( \sqrt{4} \)
(4 x 8)\( \sqrt{2 \times 4} \)
32\( \sqrt{8} \)

Now we need to simplify the radical:

32\( \sqrt{8} \)
32\( \sqrt{2 \times 4} \)
32\( \sqrt{2 \times 2^2} \)
(32)(2)\( \sqrt{2} \)
64\( \sqrt{2} \)

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

7a³ + 8a³
(7 + 8)a³
15a³

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{4}{9} \) x \( \frac{3}{7} \) = \( \frac{4 x 3}{9 x 7} \) = \( \frac{12}{63} \) = \(\frac{4}{21}\)