A factorial has the form n! and is the product of the integer (n) and all the positive integers below it. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.

To simplify this fraction, first find the greatest common factor between them. The factors of 36 are [1, 2, 3, 4, 6, 9, 12, 18, 36] and the factors of 72 are [1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72]. They share 9 factors [1, 2, 3, 4, 6, 9, 12, 18, 36] making 36 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{36}{72} \) = \( \frac{\frac{36}{36}}{\frac{72}{36}} \) = \( \frac{1}{2} \)

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

\( \frac{4}{7} \) x \( \frac{3}{5} \) = \( \frac{4 x 3}{7 x 5} \) = \( \frac{12}{35} \) = \(\frac{12}{35}\)

If 32% of the town's 47,000 voters cast ballots the number of votes cast is:

(\( \frac{32}{100} \)) x 47,000 = \( \frac{1,504,000}{100} \) = 15,040

The mayor got 60% of the votes cast which is:

(\( \frac{60}{100} \)) x 15,040 = \( \frac{902,400}{100} \) = 9,024 votes.