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

-y⁷ x 4y⁴
(-1 x 4)y^{(7 + 4)}
-4y¹¹

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 30 meters so the equation becomes: 2w + 2h = 30.

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

2w + 2h = 30
w + h = \( \frac{30}{2} \)
w + h = 15
w = 15 - h

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

w = 15 - 2w
3w = 15
w = \( \frac{15}{3} \)
w = 5

Since h = 2w that makes h = (2 x 5) = 10 and the area = h x w = 5 x 10 = 50 m²

To fill a 12 gallon tank exactly halfway you'll need 6 gallons of fuel. Each fuel can holds 1\(\frac{1}{2}\) gallons so:

cans = \( \frac{6 \text{ gallons}}{1\frac{1}{2} \text{ gallons}} \) = 4

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.

By buying two shirts, Alex will save $39 x \( \frac{5}{100} \) = \( \frac{$39 x 5}{100} \) = \( \frac{$195}{100} \) = $1.95 on the second shirt.

So, his total cost will be
$39.00 + ($39.00 - $1.95)
$39.00 + $37.05
$76.05