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.

The area of a circle is given by the formula A = πr² where r is the radius of the circle. The radius of a circle is its diameter divided by two so A = π(\( \frac{d}{2} \))². If the diameter of the logo increases by 60% the radius (and, consequently, the total area) increases by \( \frac{60\text{%}}{2} \) = 30%

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).

To simplify this fraction, first find the greatest common factor between them. The factors of 16 are [1, 2, 4, 8, 16] and the factors of 80 are [1, 2, 4, 5, 8, 10, 16, 20, 40, 80]. They share 5 factors [1, 2, 4, 8, 16] making 16 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{16}{80} \) = \( \frac{\frac{16}{16}}{\frac{80}{16}} \) = \( \frac{1}{5} \)

To find the average of these 4 numbers add them together then divide by 4:

\( \frac{9 + 3 + 10 + 2}{4} \) = \( \frac{24}{4} \) = 6