What is 680 to the Power of 3? Step-by-Step Calculation
Understanding exponentiation, or raising a number to a certain power, is a fundamental concept in mathematics. In this guide, we will explore the step-by-step calculation process for the expression "680 to the power of 3." We'll break down the concept, explain the calculation method, and discuss the significance of this mathematical operation.
Answer: 680 to the Power of 3 is 314432000
Step 1: Understanding Exponents
Step 2: The Calculation Process
Calculating 680^3 is straightforward. Follow these steps:
- Start with 680 to the power of 3.
- Multiply 1 by 680 to get 680.
- Multiply 680 by 680 to get 462400.
- Multiply 462400 by 680 to get 314432000.
- The final result is 314432000.
Step 3: Practical Applications
In science and engineering, exponentiation is used to represent quantities like distances, areas, and volumes.
In computer science, it's crucial for understanding data storage capacities and memory sizes.
In finance, it plays a role in compound interest calculations and investment growth projections.
In everyday life, it's applicable when dealing with measurements and large quantities
Frequently Asked Questions
What does "680 to the power of 3" mean?
680 to the power of 3" (680^3) is a mathematical expression that signifies multiplying the base number, 680, by itself three times. It's equivalent to 680 x 680 x 680, which equals 314432000.
How is "680 to the power of 3" calculated?
Calculating 680^3 is done by multiplying 680 by itself three times. So, 680^3 = 680 x 680 x 680, resulting in 314432000.
Can I calculate "680 to the power of 3" with negative exponents?
Negative exponents indicate taking the reciprocal of the base raised to the positive exponent. For example, 680^(-3) is equivalent to 1 / (680^3), which is 1/314432000.
Important results
| 1-10^2 | Result |
|---|---|
| 1^2 | 1 |
| 2^2 | 4 |
| 3^2 | 9 |
| 4^2 | 16 |
| 5^2 | 25 |
| 6^2 | 36 |
| 7^2 | 49 |
| 8^2 | 64 |
| 9^2 | 81 |
| 10^2 | 100 |
| 1-10^3 | Result |
|---|---|
| 1^3 | 1 |
| 2^3 | 8 |
| 3^3 | 27 |
| 4^3 | 64 |
| 5^3 | 125 |
| 6^3 | 216 |
| 7^3 | 343 |
| 8^3 | 512 |
| 9^3 | 729 |
| 10^3 | 1000 |
| 1-10^4 | Result |
|---|---|
| 1^4 | 1 |
| 2^4 | 16 |
| 3^4 | 81 |
| 4^4 | 256 |
| 5^4 | 625 |
| 6^4 | 1296 |
| 7^4 | 2401 |
| 8^4 | 4096 |
| 9^4 | 6561 |
| 10^4 | 10000 |
| 1-10^5 | Result |
|---|---|
| 1^5 | 1 |
| 2^5 | 32 |
| 3^5 | 243 |
| 4^5 | 1024 |
| 5^5 | 3125 |
| 6^5 | 7776 |
| 7^5 | 16807 |
| 8^5 | 32768 |
| 9^5 | 59049 |
| 10^5 | 100000 |