To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50] and the first few multiples of 7 are [7, 14, 21, 28, 35, 42, 49, 56, 63, 70]. The first few multiples they share are [35, 70] making 35 the smallest multiple 5 and 7 share.

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

\( \frac{5 x 7}{5 x 7} \) + \( \frac{3 x 5}{7 x 5} \)

\( \frac{35}{35} \) + \( \frac{15}{35} \)

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

\( \frac{35 + 15}{35} \) = \( \frac{50}{35} \) = 1\(\frac{3}{7}\)

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).

To raise a term with an exponent to another exponent, retain the base and multiply the exponents:

36% of the water consumption is industrial use and 14% is personal use so (36% - 14%) = 22% more water is used for industrial purposes. 25,000 gallons are consumed daily so industry consumes \( \frac{22}{100} \) x 25,000 gallons = 5,500 gallons.

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:

3y² + 3y²
(3 + 3)y²
6y²