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:

-4a⁶ x 6a³
(-4 x 6)a^{(6 + 3)}
-24a⁹

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 = \( \frac{390mi}{65mph} \)
6 hours

April scored 90% on the test meaning she earned 90% of the possible points on the test. There were 90 possible points on the test so she earned 90 x 0.9 = 81 points. Each question is worth 3 points so she got \( \frac{81}{3} \) = 27 questions right.

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{3}{9} \) x \( \frac{1}{8} \) = \( \frac{3 x 1}{9 x 8} \) = \( \frac{3}{72} \) = \(\frac{1}{24}\)

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.