- Understand that \(15^3\) is the product \(15 \times 15 \times 15\).
- Calculate \(15 \times 15 = 225\).
- Complete the final multiplication: \(225 \times 15 = 3375\).
- The final value is \(\boxed{3375}\).
Explanation
- Understanding the Problem and Data Analysis
The objective is to calculate the value of \(15^3\). This expression represents fifteen raised to the third power, which means we multiply the number fifteen by itself three times. We can write this as:
\[15^3 = 15 \times 15 \times 15\]
Our analysis requires us to first calculate the product of \(15 \times 15\), and then multiply that result by another factor of 15.
- Performing the Calculation
First, calculate \(15 \times 15\):
\[15 \times 15 = 225\]
Next, multiply this product by 15:
\[225 \times 15 = 3375\]
Thus, the value of \(15^3\) is 3375. Comparing this to the given choices, we see that it corresponds to the first option.
- Conclusion
The calculations confirm that \(15^3 = 3375\). This matches the first option provided in the problem statement. The final result is \(\boxed{3375}\).
Examples
Calculating powers is essential in many areas, such as determining volume. If you have a cube with a side length of 15 cm, its volume is found by cubing the side length: \(V = s^3 = 15^3 = 3375 \text{ cm}^3\). This calculation helps in fields ranging from architecture to product packaging design.