To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50]. The first few multiples they share are [15, 30, 45, 60, 75] making 15 the smallest multiple 3 and 5 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{5 x 5}{3 x 5} \) - \( \frac{7 x 3}{5 x 3} \)

\( \frac{25}{15} \) - \( \frac{21}{15} \)

Now, because the fractions share a common denominator, you can subtract them:

\( \frac{25 - 21}{15} \) = \( \frac{4}{15} \) = \(\frac{4}{15}\)

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

\( \frac{18\sqrt{6}}{9\sqrt{2}} \)
\( \frac{18}{9} \) \( \sqrt{\frac{6}{2}} \)
2 \( \sqrt{3} \)

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 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 number with an exponent (b^e) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b¹ = b) and a base with an exponent of 0 equals 1 ( (b⁰ = 1).