If the side lengths of a cube are 16 feet, what is the correct way to write the expression to represent the volume of the cube in exponential form? 16 ⋅ 3 16 ⋅ 16 ⋅ 16 163 316
The Correct Answer and Explanation is:
The correct way to write the expression to represent the volume of the cube in exponential form is 16³.
Explanation:
The volume of a cube can be calculated using the formula:
[
\text{Volume of a cube} = \text{side length}^3
]
This formula is based on the fact that a cube is a three-dimensional object with all sides of equal length. When we calculate the volume of a cube, we multiply the length of one side by itself three times (since a cube has three dimensions: length, width, and height).
In your question, the side length of the cube is given as 16 feet. So, the volume of the cube would be calculated as:
[
\text{Volume} = 16 \times 16 \times 16
]
This expression represents multiplying the side length by itself three times. Instead of writing it out as (16 \times 16 \times 16), we can use exponential notation to simplify the expression. The general rule is that when a number is multiplied by itself multiple times, it can be written as the number raised to the power of the number of times it is multiplied. In this case, the side length is 16 and it is multiplied by itself 3 times, so the expression becomes:
[
16^3
]
This is the exponential form of the volume of the cube.
Why Other Options Are Incorrect:
- 16 ⋅ 3: This represents the side length (16) multiplied by 3, which is not how the volume of a cube is calculated. This expression would give the perimeter of a 2D square, not the volume of a 3D cube.
- 16 ⋅ 16 ⋅ 16: This is the correct expanded form of the volume formula. While accurate, it is not in exponential form. Exponential notation is a shorthand for repeating the same number multiple times, so it should be written as (16^3).
- 163: This appears to be an attempt at writing the exponential form but is formatted incorrectly. It would read as “16 followed by the number 3,” which is not the correct way to represent an exponentiation. The correct format is 16³.
- 316: This is a completely different expression and does not represent the volume of the cube.
Thus, the correct and most simplified form is 16³, which represents the volume of the cube with side length 16 feet.