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

\( \frac{5a^5}{2a^3} \)
\( \frac{5}{2} \) a^{(5 - 3)}
2\(\frac{1}{2}\)a²

The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.

You have 8 out of the total of 200 raffle tickets sold so you have a (\( \frac{8}{200} \)) x 100 = \( \frac{8 \times 100}{200} \) = \( \frac{800}{200} \) = 4% chance to win the raffle.

The commutative property states that, when adding or multiplying numbers, the order in which they're added or multiplied does not matter. For example, 3 + 4 and 4 + 3 give the same result, as do 3 x 4 and 4 x 3.

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90] and the first few multiples of 15 are [15, 30, 45, 60, 75, 90]. The first few multiples they share are [45, 90] making 45 the smallest multiple 9 and 15 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{6 x 5}{9 x 5} \) - \( \frac{2 x 3}{15 x 3} \)

\( \frac{30}{45} \) - \( \frac{6}{45} \)

Now, because the fractions share a common denominator, you can subtract them:

\( \frac{30 - 6}{45} \) = \( \frac{24}{45} \) = \(\frac{8}{15}\)