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:

-4c⁵ x 8c⁴
(-4 x 8)c^{(5 + 4)}
-32c⁹

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.

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 divide terms with radicals, divide the coefficients and radicands separately:

\( \frac{12\sqrt{16}}{6\sqrt{4}} \)
\( \frac{12}{6} \) \( \sqrt{\frac{16}{4}} \)
2 \( \sqrt{4} \)

To add these radicals together their radicands must be the same:

7\( \sqrt{8} \) + 5\( \sqrt{2} \)
7\( \sqrt{4 \times 2} \) + 5\( \sqrt{2} \)
7\( \sqrt{2^2 \times 2} \) + 5\( \sqrt{2} \)
(7)(2)\( \sqrt{2} \) + 5\( \sqrt{2} \)
14\( \sqrt{2} \) + 5\( \sqrt{2} \)

Now that the radicands are identical, you can add them together: