The problem asks to calculate the volume of a cube using exponents, and the diagram shows a large cube decomposing into smaller cubes. To solve this:

1. Step 1: Identify the dimensions of the cube. The large cube appears to be divided into smaller cubes. Each row and layer consists of 3 small cubes. Therefore, the side length of the large cube is $3$ units.

2. Step 2: Use the volume formula for a cube. The volume $V$ of a cube is calculated using the formula:

   $V = s^3$ where $s$ is the side length of the cube.

3. Step 3: Calculate the volume. Since the side length $s = 3$, the volume is:

   $V = 3^3 = 3 \times 3 \times 3 = 27 \, \text{cubic units}$

Thus, the volume of the cube is 27 cubic units.

Would you like more details on this? Here are 5 related questions:

1. How do exponents relate to calculating the volume of a cube?
2. What happens to the volume when you double the side length of a cube?
3. How would the volume change if each smaller cube had a side length of 1 unit instead?
4. Can you apply the same exponent rule to other 3D shapes like a rectangular prism?
5. How does decomposing the cube into smaller parts help in visualizing its volume?

Tip: Always remember that the volume of any cube is simply the cube of its side length!