The factors of 64 are [1, 2, 4, 8, 16, 32, 64] and the factors of 72 are [1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72]. They share 4 factors [1, 2, 4, 8] making 8 the greatest factor 64 and 72 have in common.

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:

9y⁶ x 3y²
(9 x 3)y^{(6 + 2)}
27y⁸

If a single cook can bake 4 large cakes per hour and the kitchen is available for 3 hours, a single cook can bake 4 x 3 = 12 large cakes during that time. 25 large cakes are needed for the party so \( \frac{25}{12} \) = 2\(\frac{1}{12}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 18 small cakes per hour and the kitchen is available for 3 hours, a single cook can bake 18 x 3 = 54 small cakes during that time. 470 small cakes are needed for the party so \( \frac{470}{54} \) = 8\(\frac{19}{27}\) cooks are needed to bake the required number of small cakes.

Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 3 + 9 = 12 cooks.

66% of the water consumption is industrial use and 34% is personal use so (66% - 34%) = 32% more water is used for industrial purposes. 5,000 gallons are consumed daily so industry consumes \( \frac{32}{100} \) x 5,000 gallons = 1,600 gallons.

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.