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.

To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:

\( \frac{-3b^9}{b^3} \)
\( \frac{-3}{1} \) b^{(9 - 3)}
-3b⁶

The area of a rectangle is width (w) x height (h). In this problem we know that the rectangle is twice as long as it is wide so h = 2w. The perimeter of a rectangle is 2w + 2h and we know that the perimeter of this rectangle is 36 meters so the equation becomes: 2w + 2h = 36.

Putting these two equations together and solving for width (w):

2w + 2h = 36
w + h = \( \frac{36}{2} \)
w + h = 18
w = 18 - h

From the question we know that h = 2w so substituting 2w for h gives us:

w = 18 - 2w
3w = 18
w = \( \frac{18}{3} \)
w = 6

Since h = 2w that makes h = (2 x 6) = 12 and the area = h x w = 6 x 12 = 72 m²

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.

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:

-6z⁶ - 8z⁶
(-6 - 8)z⁶
-14z⁶