To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40]. The first few multiples they share are [4, 8, 12, 16, 20] making 4 the smallest multiple 2 and 4 share.

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

\( \frac{5 x 2}{2 x 2} \) + \( \frac{6 x 1}{4 x 1} \)

\( \frac{10}{4} \) + \( \frac{6}{4} \)

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

\( \frac{10 + 6}{4} \) = \( \frac{16}{4} \) = 4

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:

1b⁴ + 5b⁴
(1 + 5)b⁴
6b⁴

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

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so subtract the coefficients and retain the base and exponent:

-5a⁶ - 9a⁶
(-5 - 9)a⁶
-14a⁶

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

Solving for distance:

distance = \( \text{speed} \times \text{time} \)
distance = \( 65mph \times 9h \)
585 miles