The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).

To simplify this fraction, first find the greatest common factor between them. The factors of 20 are [1, 2, 4, 5, 10, 20] and the factors of 44 are [1, 2, 4, 11, 22, 44]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{20}{44} \) = \( \frac{\frac{20}{4}}{\frac{44}{4}} \) = \( \frac{5}{11} \)

The factors of 32 are [1, 2, 4, 8, 16, 32] and the factors of 24 are [1, 2, 3, 4, 6, 8, 12, 24]. They share 4 factors [1, 2, 4, 8] making 8 the greatest factor 32 and 24 have in common.

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:

-9x³ x 4x⁷
(-9 x 4)x^{(3 + 7)}
-36x¹⁰

To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.