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:

\( \frac{-c^6}{2c^2} \)
\( \frac{-1}{2} \) c^{(6 - 2)}
-\(\frac{1}{2}\)c⁴

The ratio of football cards to baseball cards is 3:2 and the ratio of baseball cards to basketball cards is 3:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 9:6 and the ratio of baseball cards to basketball cards as 6:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 9:6, 6:2 which reduces to 9:2.

61% of the water consumption is industrial use and 32% is personal use so (61% - 32%) = 29% more water is used for industrial purposes. 50,000 gallons are consumed daily so industry consumes \( \frac{29}{100} \) x 50,000 gallons = 14,499 gallons.

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

\( \frac{2}{8} \) ÷ \( \frac{4}{5} \) = \( \frac{2}{8} \) x \( \frac{5}{4} \)

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

\( \frac{2}{8} \) x \( \frac{5}{4} \) = \( \frac{2 x 5}{8 x 4} \) = \( \frac{10}{32} \) = \(\frac{5}{16}\)

The greatest common factor (GCF) is the greatest factor that divides two integers.