A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:

\( \frac{2!}{6!} \)
\( \frac{2 \times 1}{6 \times 5 \times 4 \times 3 \times 2 \times 1} \)
\( \frac{1}{6 \times 5 \times 4 \times 3} \)
\( \frac{1}{360} \)

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 = \( \frac{280mi}{70mph} \)
4 hours

By buying two shirts, Roger will save $50 x \( \frac{50}{100} \) = \( \frac{$50 x 50}{100} \) = \( \frac{$2500}{100} \) = $25.00 on the second shirt.

So, his total cost will be
$50.00 + ($50.00 - $25.00)
$50.00 + $25.00
$75.00

To subtract 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 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80]. The first few multiples they share are [24, 48, 72, 96] making 24 the smallest multiple 6 and 8 share.

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

\( \frac{5 x 4}{6 x 4} \) - \( \frac{9 x 3}{8 x 3} \)

\( \frac{20}{24} \) - \( \frac{27}{24} \)

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

\( \frac{20 - 27}{24} \) = \( \frac{-7}{24} \) = -\(\frac{7}{24}\)

A number with an exponent (b^e) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b¹ = b) and a base with an exponent of 0 equals 1 ( (b⁰ = 1).