40% of the water consumption is industrial use and 26% is personal use so (40% - 26%) = 14% more water is used for industrial purposes. 45,000 gallons are consumed daily so industry consumes \( \frac{14}{100} \) x 45,000 gallons = 6,300 gallons.

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

-2a³ - 5a³
(-2 - 5)a³
-7a³

To multiply terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:

x⁴ x 5x⁷
(1 x 5)x^{(4 + 7)}
5x¹¹

The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] 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 [21, 42, 63, 84] making 21 the smallest multiple 3 and 7 have in common.

A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:

\( \frac{6!}{2!} \)
\( \frac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{2 \times 1} \)
\( \frac{6 \times 5 \times 4 \times 3}{1} \)
\( 6 \times 5 \times 4 \times 3 \)
360