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

\( \frac{1}{8} \) ÷ \( \frac{2}{8} \) = \( \frac{1}{8} \) x \( \frac{8}{2} \)

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

\( \frac{1}{8} \) x \( \frac{8}{2} \) = \( \frac{1 x 8}{8 x 2} \) = \( \frac{8}{16} \) = \(\frac{1}{2}\)

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:

-1y⁴ + 3y⁴
(-1 + 3)y⁴
2y⁴

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 12 are [12, 24, 36, 48, 60, 72, 84, 96]. The first few multiples they share are [12, 24, 36, 48, 60] making 12 the smallest multiple 6 and 12 share.

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

\( \frac{8 x 2}{6 x 2} \) + \( \frac{3 x 1}{12 x 1} \)

\( \frac{16}{12} \) + \( \frac{3}{12} \)

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

\( \frac{16 + 3}{12} \) = \( \frac{19}{12} \) = 1\(\frac{7}{12}\)

40% of the water consumption is industrial use and 24% is personal use so (40% - 24%) = 16% more water is used for industrial purposes. 35,000 gallons are consumed daily so industry consumes \( \frac{16}{100} \) x 35,000 gallons = 5,600 gallons.

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