32% of the water consumption is industrial use and 11% is personal use so (32% - 11%) = 21% more water is used for industrial purposes. 35,000 gallons are consumed daily so industry consumes \( \frac{21}{100} \) x 35,000 gallons = 7,350 gallons.

The factors of 48 are [1, 2, 3, 4, 6, 8, 12, 16, 24, 48] and the factors of 48 are [1, 2, 3, 4, 6, 8, 12, 16, 24, 48]. They share 10 factors [1, 2, 3, 4, 6, 8, 12, 16, 24, 48] making 48 the greatest factor 48 and 48 have in common.

A factor is a positive integer that divides evenly into a given number. For example, the factors of 8 are 1, 2, 4, and 8.

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80] and the first few multiples of 16 are [16, 32, 48, 64, 80, 96]. The first few multiples they share are [16, 32, 48, 64, 80] making 16 the smallest multiple 8 and 16 share.

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

\( \frac{3 x 2}{8 x 2} \) + \( \frac{2 x 1}{16 x 1} \)

\( \frac{6}{16} \) + \( \frac{2}{16} \)

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

\( \frac{6 + 2}{16} \) = \( \frac{8}{16} \) = \(\frac{1}{2}\)

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