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:

8a³ x 2a⁷
(8 x 2)a^{(3 + 7)}
16a¹⁰

A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:

\( \frac{3!}{2!} \)
\( \frac{3 \times 2 \times 1}{2 \times 1} \)
\( \frac{3}{1} \)
3

The commutative property states that, when adding or multiplying numbers, the order in which they're added or multiplied does not matter. For example, 3 + 4 and 4 + 3 give the same result, as do 3 x 4 and 4 x 3.

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

3\( \sqrt{112} \) + 5\( \sqrt{7} \)
3\( \sqrt{16 \times 7} \) + 5\( \sqrt{7} \)
3\( \sqrt{4^2 \times 7} \) + 5\( \sqrt{7} \)
(3)(4)\( \sqrt{7} \) + 5\( \sqrt{7} \)
12\( \sqrt{7} \) + 5\( \sqrt{7} \)

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

The equation for this sequence is:

a_n = a_n-1 + 3(n - 1)

where n is the term's order in the sequence, a_n is the value of the term, and a_n-1 is the value of the term before a_n. This makes the next number:

a₆ = a₅ + 3(6 - 1)
a₆ = 31 + 3(5)
a₆ = 46