In this section, you will use formulas and the laws of exponents to solve problems.

Directions: Read each problem. Determine the answer to each problem using the mathematics reference chart in the previous section and the laws of exponents.

1. The area of a rectangle measures 36x⁵y⁷. The length of the rectangle measures 4x²y³. What is the width of the rectangle?
   

   Interactive popup. Assistance may be required. Click to see the solution. The formula for the area of a rectangle is: A = l × w
   Solve the formula for w: w = a over l A l
   Use the laws of exponents to solve the problem:
   w = 36x to the fifth y to the seventh over 4x squared y cubed 36x⁵y⁷ 4x²y³
   w = 9x³y⁴

2. The height of a trapezoid is 4ab³. The bases of the trapezoid are 2ab and 5ab respectively. What is the area of the trapezoid?
   

   Interactive popup. Assistance may be required. Click to see the solution. Formula for the Area of a Trapezoid: numerator: the quantity b sub 1 plus b sub 2 all times h; demonimator: 2 (b₁ + b₂)h 2
   Substitute: A = numerator: the quantity 2ab plus 5ab all times 4ab cubed; demonimator: 2 (2ab + 5ab)4ab³ 2
   A = numerator: 7ab times 4ab cubed; demonimator: 2 (7ab)4ab³ 2
   A = numerator: 28 a squared b to the fourth power; demonimator: 2 28a²b⁴ 2
   A = 14a²b⁴