What is 21 to the Power of 10? 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 "21 to the power of 10." We'll break down the concept, explain the calculation method, and discuss the significance of this mathematical operation.
Answer: 21 to the Power of 10 is 16679880978201
Step 1: Understanding Exponents
Step 2: The Calculation Process
Calculating 21^10 is straightforward. Follow these steps:
- Start with 21 to the power of 10.
- Multiply 1 by 21 to get 21.
- Multiply 21 by 21 to get 441.
- Multiply 441 by 21 to get 9261.
- Multiply 9261 by 21 to get 194481.
- Multiply 194481 by 21 to get 4084101.
- Multiply 4084101 by 21 to get 85766121.
- Multiply 85766121 by 21 to get 1801088541.
- Multiply 1801088541 by 21 to get 37822859361.
- Multiply 37822859361 by 21 to get 794280046581.
- Multiply 794280046581 by 21 to get 16679880978201.
- The final result is 16679880978201.
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 "21 to the power of 10" mean?
21 to the power of 10" (21^10) is a mathematical expression that signifies multiplying the base number, 21, by itself three times. It's equivalent to 21 x 21 x 21, which equals 16679880978201.
How is "21 to the power of 10" calculated?
Calculating 21^10 is done by multiplying 21 by itself three times. So, 21^10 = 21 x 21 x 21, resulting in 16679880978201.
Can I calculate "21 to the power of 10" with negative exponents?
Negative exponents indicate taking the reciprocal of the base raised to the positive exponent. For example, 21^(-10) is equivalent to 1 / (21^10), which is 1/16679880978201.
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 |