Average speed in miles per hour is the number of miles traveled divided by the number of hours:

Solving for time:

time = \( \frac{\text{distance}}{\text{speed}} \)
time = \( \frac{75mi}{15mph} \)
5 hours

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90]. The first few multiples they share are [9, 18, 27, 36, 45] making 9 the smallest multiple 3 and 9 share.

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

\( \frac{8 x 3}{3 x 3} \) - \( \frac{3 x 1}{9 x 1} \)

\( \frac{24}{9} \) - \( \frac{3}{9} \)

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

\( \frac{24 - 3}{9} \) = \( \frac{21}{9} \) = 2\(\frac{1}{3}\)

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:

3a⁵ x 4a⁴
(3 x 4)a^{(5 + 4)}
12a⁹

The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).

To find the average of these 4 numbers add them together then divide by 4:

\( \frac{12 + 10 + 14 + 8}{4} \) = \( \frac{44}{4} \) = 11