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:

-9y³ x 5y⁴
(-9 x 5)y^{(3 + 4)}
-45y⁷

The commutative property states that, when adding or multiplying numbers, the order in which they're added or multiplied does not matter. For example, 3 + 4 and 4 + 3 give the same result, as do 3 x 4 and 4 x 3.

If a single cook can bake 2 large cakes per hour and the kitchen is available for 2 hours, a single cook can bake 2 x 2 = 4 large cakes during that time. 23 large cakes are needed for the party so \( \frac{23}{4} \) = 5\(\frac{3}{4}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 19 small cakes per hour and the kitchen is available for 2 hours, a single cook can bake 19 x 2 = 38 small cakes during that time. 100 small cakes are needed for the party so \( \frac{100}{38} \) = 2\(\frac{12}{19}\) 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 6 + 3 = 9 cooks.

37% of the water consumption is industrial use and 14% is personal use so (37% - 14%) = 23% more water is used for industrial purposes. 30,000 gallons are consumed daily so industry consumes \( \frac{23}{100} \) x 30,000 gallons = 6,900 gallons.

The greatest common factor (GCF) is the greatest factor that divides two integers.