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.

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).

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{2}{7} \) x \( \frac{1}{7} \) = \( \frac{2 x 1}{7 x 7} \) = \( \frac{2}{49} \) = \(\frac{2}{49}\)

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

\( \frac{21\sqrt{27}}{3\sqrt{9}} \)
\( \frac{21}{3} \) \( \sqrt{\frac{27}{9}} \)
7 \( \sqrt{3} \)

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.