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:

-6z³ x 5z⁷
(-6 x 5)z^{(3 + 7)}
-30z¹⁰

The equation for this sequence is:

a_n = a_n-1 + 4(n - 1)

where n is the term's order in the sequence, a_n is the value of the term, and a_n-1 is the value of the term before a_n. This makes the next number:

a₆ = a₅ + 4(6 - 1)
a₆ = 41 + 4(5)
a₆ = 61

To divide terms with radicals, divide the coefficients and radicands separately:

\( \frac{12\sqrt{15}}{6\sqrt{5}} \)
\( \frac{12}{6} \) \( \sqrt{\frac{15}{5}} \)
2 \( \sqrt{3} \)

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 12 are [12, 24, 36, 48, 60, 72, 84, 96]. The first few multiples they share are [12, 24, 36, 48, 60] making 12 the smallest multiple 6 and 12 share.

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

\( \frac{2 x 2}{6 x 2} \) + \( \frac{9 x 1}{12 x 1} \)

\( \frac{4}{12} \) + \( \frac{9}{12} \)

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

\( \frac{4 + 9}{12} \) = \( \frac{13}{12} \) = 1\(\frac{1}{12}\)

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 = \( 20mph \times 3h \)
60 miles