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:

\( \frac{-4a^5}{2a^2} \)
\( \frac{-4}{2} \) a^{(5 - 2)}
-2a³

First, solve for \( \left|y - 2\right| \):

\( \left|y - 2\right| \) + 4 = 9
\( \left|y - 2\right| \) = 9 - 4
\( \left|y - 2\right| \) = 5

The value inside the absolute value brackets can be either positive or negative so (y - 2) must equal + 5 or -5 for \( \left|y - 2\right| \) to equal 5:

So, y = -3 or y = 7.

A ratio of 2:1 means that there are 2 home fans for every one visiting fan. So, of every 3 fans, 2 are home fans and \( \frac{2}{3} \) of every fan in the stadium is a home fan:

35,000 fans x \( \frac{2}{3} \) = \( \frac{70000}{3} \) = 23,333 fans.

The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:

interest = annual interest rate x loan amount

i = (\( \frac{6}{100} \)) x $1,300
i = 0.04 x $1,300
i = $52

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 48 meters so the equation becomes: 2w + 2h = 48.

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

2w + 2h = 48
w + h = \( \frac{48}{2} \)
w + h = 24
w = 24 - h

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

w = 24 - 2w
3w = 24
w = \( \frac{24}{3} \)
w = 8

Since h = 2w that makes h = (2 x 8) = 16 and the area = h x w = 8 x 16 = 128 m²