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

First, solve for \( \left|c - 6\right| \):

\( \left|c - 6\right| \) + 6 = -4
\( \left|c - 6\right| \) = -4 - 6
\( \left|c - 6\right| \) = -10

The value inside the absolute value brackets can be either positive or negative so (c - 6) must equal - 10 or --10 for \( \left|c - 6\right| \) to equal -10:

So, c = 16 or c = -4.

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 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:

4a⁴ x 9a²
(4 x 9)a^{(4 + 2)}
36a⁶

The first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [20, 40, 60, 80] making 20 the smallest multiple 4 and 10 have in common.