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

\( \frac{3}{7} \) x \( \frac{2}{8} \) = \( \frac{3 x 2}{7 x 8} \) = \( \frac{6}{56} \) = \(\frac{3}{28}\)

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

To subtract these radicals together their radicands must be the same:

2\( \sqrt{50} \) - 3\( \sqrt{2} \)
2\( \sqrt{25 \times 2} \) - 3\( \sqrt{2} \)
2\( \sqrt{5^2 \times 2} \) - 3\( \sqrt{2} \)
(2)(5)\( \sqrt{2} \) - 3\( \sqrt{2} \)
10\( \sqrt{2} \) - 3\( \sqrt{2} \)

Now that the radicands are identical, you can subtract them:

29% of the water consumption is industrial use and 14% is personal use so (29% - 14%) = 15% more water is used for industrial purposes. 45,000 gallons are consumed daily so industry consumes \( \frac{15}{100} \) x 45,000 gallons = 6,750 gallons.

The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).