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 simplify a radical, factor out the perfect squares:

\( \sqrt{32} \)
\( \sqrt{16 \times 2} \)
\( \sqrt{4^2 \times 2} \)
4\( \sqrt{2} \)

Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):

2 + (3 + 3) ÷ 4 x 5 - 4²
P: 2 + (6) ÷ 4 x 5 - 4²
E: 2 + 6 ÷ 4 x 5 - 16
MD: 2 + \( \frac{6}{4} \) x 5 - 16
MD: 2 + \( \frac{30}{4} \) - 16
AS: \( \frac{8}{4} \) + \( \frac{30}{4} \) - 16
AS: \( \frac{38}{4} \) - 16
AS: \( \frac{38 - 64}{4} \)
\( \frac{-26}{4} \)
-6\(\frac{1}{2}\)

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

7\( \sqrt{8} \) x 2\( \sqrt{5} \)
(7 x 2)\( \sqrt{8 \times 5} \)
14\( \sqrt{40} \)

Now we need to simplify the radical:

14\( \sqrt{40} \)
14\( \sqrt{10 \times 4} \)
14\( \sqrt{10 \times 2^2} \)
(14)(2)\( \sqrt{10} \)
28\( \sqrt{10} \)

If 74% of the town's 32,000 voters cast ballots the number of votes cast is:

(\( \frac{74}{100} \)) x 32,000 = \( \frac{2,368,000}{100} \) = 23,680

The mayor got 75% of the votes cast which is:

(\( \frac{75}{100} \)) x 23,680 = \( \frac{1,776,000}{100} \) = 17,760 votes.