If a single cook can bake 5 large cakes per hour and the kitchen is available for 3 hours, a single cook can bake 5 x 3 = 15 large cakes during that time. 34 large cakes are needed for the party so \( \frac{34}{15} \) = 2\(\frac{4}{15}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 18 small cakes per hour and the kitchen is available for 3 hours, a single cook can bake 18 x 3 = 54 small cakes during that time. 320 small cakes are needed for the party so \( \frac{320}{54} \) = 5\(\frac{25}{27}\) cooks are needed to bake the required number of small cakes.

Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 3 + 6 = 9 cooks.

A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.

To simplify this fraction, first find the greatest common factor between them. The factors of 16 are [1, 2, 4, 8, 16] and the factors of 72 are [1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72]. They share 4 factors [1, 2, 4, 8] making 8 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{16}{72} \) = \( \frac{\frac{16}{8}}{\frac{72}{8}} \) = \( \frac{2}{9} \)

To multiply terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:

-c⁶ x 4c⁷
(-1 x 4)c^{(6 + 7)}
-4c¹³

If 72% of the town's 24,000 voters cast ballots the number of votes cast is:

(\( \frac{72}{100} \)) x 24,000 = \( \frac{1,728,000}{100} \) = 17,280

The mayor got 62% of the votes cast which is:

(\( \frac{62}{100} \)) x 17,280 = \( \frac{1,071,360}{100} \) = 10,714 votes.