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:

-6c⁶ x 2c³
(-6 x 2)c^{(6 + 3)}
-12c⁹

The number of students taking German or Spanish is 9 + 13 = 22. Of that group of 22, 6 are taking both languages so they've been counted twice (once in the German group and once in the Spanish group). Subtracting them out leaves 22 - 6 = 16 who are taking at least one language. 25 - 16 = 9 students who are not taking either language.

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40]. The first few multiples they share are [4, 8, 12, 16, 20] making 4 the smallest multiple 2 and 4 share.

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

\( \frac{4 x 2}{2 x 2} \) - \( \frac{2 x 1}{4 x 1} \)

\( \frac{8}{4} \) - \( \frac{2}{4} \)

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

\( \frac{8 - 2}{4} \) = \( \frac{6}{4} \) = 1\(\frac{1}{2}\)

To add these distances, they must share the same unit so first you need to first convert the swim distance from meters (m) to kilometers (km) before adding it to the bike and run distances which are already in km. To convert 100 meters to kilometers, divide the distance by 1000 to get 0.1km then add the remaining distances:

total distance = swim + bike + run
total distance = 0.1km + 20.1km + 16.3km
total distance = 36.5km

The factors of a number are all positive integers that divide evenly into the number. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24.