A chest has 8 containers. Each container has 8 boxes. Each box has 8 bottles. Each bottle has 8 quarters.
a) write a power to describe the total number of quarters.
b) what is the value of the money in the chest?
a) 8^4 (8 to the fourth power).
b) ($0.25) x 8^4
a) To calculate the total number of quarters, we need to multiply the number of containers, the number of boxes in each container, the number of bottles in each box, and the number of quarters in each bottle. Therefore, we can express it as a power:
Total number of quarters = (Number of containers) * (Number of boxes per container) * (Number of bottles per box) * (Number of quarters per bottle)
Total number of quarters = 8^1 * 8^2 * 8^3 * 8^4
Simplifying the expression, we can add the exponents:
Total number of quarters = 8^(1 + 2 + 3 + 4)
b) To calculate the value of the money in the chest, we need to know the value of each quarter. Assuming each quarter is worth $0.25, we can calculate the total value by multiplying the total number of quarters by the value of each quarter:
Value of the money in the chest = (Total number of quarters) * (Value of each quarter)
Remember that the total number of quarters is given by 8^(1 + 2 + 3 + 4), as calculated in part a).