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 convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.

A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.

The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.

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

3\( \sqrt{48} \) - 6\( \sqrt{3} \)
3\( \sqrt{16 \times 3} \) - 6\( \sqrt{3} \)
3\( \sqrt{4^2 \times 3} \) - 6\( \sqrt{3} \)
(3)(4)\( \sqrt{3} \) - 6\( \sqrt{3} \)
12\( \sqrt{3} \) - 6\( \sqrt{3} \)

Now that the radicands are identical, you can subtract them: