A factorial has the form n! and is the product of the integer (n) and all the positive integers below it. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.

To divide fractions, invert the second fraction and then multiply:

\( \frac{2}{9} \) ÷ \( \frac{1}{6} \) = \( \frac{2}{9} \) x \( \frac{6}{1} \)

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{2}{9} \) x \( \frac{6}{1} \) = \( \frac{2 x 6}{9 x 1} \) = \( \frac{12}{9} \) = 1\(\frac{1}{3}\)

The greatest common factor (GCF) is the greatest factor that divides two integers.

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:

-5a⁷ x 2a³
(-5 x 2)a^{(7 + 3)}
-10a¹⁰

To simplify this fraction, first find the greatest common factor between them. The factors of 40 are [1, 2, 4, 5, 8, 10, 20, 40] 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:

\( \frac{40}{44} \) = \( \frac{\frac{40}{4}}{\frac{44}{4}} \) = \( \frac{10}{11} \)