To multiply terms with radicals, multiply the coefficients and radicands separately:

6\( \sqrt{3} \) x 8\( \sqrt{2} \)
(6 x 8)\( \sqrt{3 \times 2} \)
48\( \sqrt{6} \)

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.

The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).

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 simplify this fraction, first find the greatest common factor between them. The factors of 28 are [1, 2, 4, 7, 14, 28] and the factors of 68 are [1, 2, 4, 17, 34, 68]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{28}{68} \) = \( \frac{\frac{28}{4}}{\frac{68}{4}} \) = \( \frac{7}{17} \)