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

If 34% of the town's 40,000 voters cast ballots the number of votes cast is:

(\( \frac{34}{100} \)) x 40,000 = \( \frac{1,360,000}{100} \) = 13,600

The mayor got 71% of the votes cast which is:

(\( \frac{71}{100} \)) x 13,600 = \( \frac{965,600}{100} \) = 9,656 votes.

You have 1 out of the total of 50 raffle tickets sold so you have a (\( \frac{1}{50} \)) x 100 = \( \frac{1 \times 100}{50} \) = \( \frac{100}{50} \) = 2% chance to win the raffle.

A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:

\( \frac{6!}{3!} \)
\( \frac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{3 \times 2 \times 1} \)
\( \frac{6 \times 5 \times 4}{1} \)
\( 6 \times 5 \times 4 \)
120

The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:

interest = annual interest rate x loan amount

i = (\( \frac{6}{100} \)) x $100
i = 0.08 x $100
i = $8