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:

\( \frac{2y^9}{6y^4} \)
\( \frac{2}{6} \) y^{(9 - 4)}
\(\frac{1}{3}\)y⁵

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 33% is personal use so (61% - 33%) = 28% more water is used for industrial purposes. 35,000 gallons are consumed daily so industry consumes \( \frac{28}{100} \) x 35,000 gallons = 9,800 gallons.

A prime number is an integer greater than 1 that has no factors other than 1 and itself. Examples of prime numbers include 2, 3, 5, 7, and 11.

Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):

3 + (2 + 5) ÷ 3 x 4 - 2²
P: 3 + (7) ÷ 3 x 4 - 2²
E: 3 + 7 ÷ 3 x 4 - 4
MD: 3 + \( \frac{7}{3} \) x 4 - 4
MD: 3 + \( \frac{28}{3} \) - 4
AS: \( \frac{9}{3} \) + \( \frac{28}{3} \) - 4
AS: \( \frac{37}{3} \) - 4
AS: \( \frac{37 - 12}{3} \)
\( \frac{25}{3} \)
8\(\frac{1}{3}\)