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.

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A number with an exponent (b^e) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b¹ = b) and a base with an exponent of 0 equals 1 ( (b⁰ = 1).

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. 40 large cakes are needed for the party so \( \frac{40}{12} \) = 3\(\frac{1}{3}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 15 small cakes per hour and the kitchen is available for 3 hours, a single cook can bake 15 x 3 = 45 small cakes during that time. 110 small cakes are needed for the party so \( \frac{110}{45} \) = 2\(\frac{4}{9}\) 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 4 + 3 = 7 cooks.

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.