To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so subtract the coefficients and retain the base and exponent:

8a⁷ - 5a⁷
(8 - 5)a⁷
3a⁷

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.

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 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.

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

5\( \sqrt{48} \) + 7\( \sqrt{3} \)
5\( \sqrt{16 \times 3} \) + 7\( \sqrt{3} \)
5\( \sqrt{4^2 \times 3} \) + 7\( \sqrt{3} \)
(5)(4)\( \sqrt{3} \) + 7\( \sqrt{3} \)
20\( \sqrt{3} \) + 7\( \sqrt{3} \)

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