To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:

\( \frac{-6a^6}{5a^4} \)
\( \frac{-6}{5} \) a^{(6 - 4)}
-1\(\frac{1}{5}\)a²

To simplify this fraction, first find the greatest common factor between them. 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 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{24}{72} \) = \( \frac{\frac{24}{24}}{\frac{72}{24}} \) = \( \frac{1}{3} \)

The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 11 are [11, 22, 33, 44, 55, 66, 77, 88, 99]. The first few multiples they share are [33, 66, 99] making 33 the smallest multiple 3 and 11 have in common.

The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.

Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):

2 + (5 + 4) ÷ 5 x 4 - 5²
P: 2 + (9) ÷ 5 x 4 - 5²
E: 2 + 9 ÷ 5 x 4 - 25
MD: 2 + \( \frac{9}{5} \) x 4 - 25
MD: 2 + \( \frac{36}{5} \) - 25
AS: \( \frac{10}{5} \) + \( \frac{36}{5} \) - 25
AS: \( \frac{46}{5} \) - 25
AS: \( \frac{46 - 125}{5} \)
\( \frac{-79}{5} \)
-15\(\frac{4}{5}\)