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:

8a⁴ - 5a⁴
(8 - 5)a⁴
3a⁴

A factor is a positive integer that divides evenly into a given number. For example, the factors of 8 are 1, 2, 4, and 8.

To simplify this fraction, first find the greatest common factor between them. The factors of 20 are [1, 2, 4, 5, 10, 20] and the factors of 60 are [1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60]. They share 6 factors [1, 2, 4, 5, 10, 20] making 20 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{20}{60} \) = \( \frac{\frac{20}{20}}{\frac{60}{20}} \) = \( \frac{1}{3} \)

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50] and the first few multiples of 7 are [7, 14, 21, 28, 35, 42, 49, 56, 63, 70]. The first few multiples they share are [35, 70] making 35 the smallest multiple 5 and 7 share.

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

\( \frac{2 x 7}{5 x 7} \) + \( \frac{2 x 5}{7 x 5} \)

\( \frac{14}{35} \) + \( \frac{10}{35} \)

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

\( \frac{14 + 10}{35} \) = \( \frac{24}{35} \) = \(\frac{24}{35}\)

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 = \( \frac{420mi}{70mph} \)
6 hours