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 = \( 45mph \times 4h \)
180 miles

To divide fractions, invert the second fraction and then multiply:

\( \frac{2}{8} \) ÷ \( \frac{1}{7} \) = \( \frac{2}{8} \) x \( \frac{7}{1} \)

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

\( \frac{2}{8} \) x \( \frac{7}{1} \) = \( \frac{2 x 7}{8 x 1} \) = \( \frac{14}{8} \) = 1\(\frac{3}{4}\)

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

4\( \sqrt{8} \) x 2\( \sqrt{2} \)
(4 x 2)\( \sqrt{8 \times 2} \)
8\( \sqrt{16} \)

Now we need to simplify the radical:

8\( \sqrt{16} \)
8\( \sqrt{4^2} \)
(8)(4)
32

The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).

To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:

\( \frac{-8c^6}{4c^2} \)
\( \frac{-8}{4} \) c^{(6 - 2)}
-2c⁴