What is 25 to the Power of 9? 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 "25 to the power of 9." We'll break down the concept, explain the calculation method, and discuss the significance of this mathematical operation.
Answer: 25 to the Power of 9 is 3814697265625
Step 1: Understanding Exponents
Step 2: The Calculation Process
Calculating 25^9 is straightforward. Follow these steps:
- Start with 25 to the power of 9.
- Multiply 1 by 25 to get 25.
- Multiply 25 by 25 to get 625.
- Multiply 625 by 25 to get 15625.
- Multiply 15625 by 25 to get 390625.
- Multiply 390625 by 25 to get 9765625.
- Multiply 9765625 by 25 to get 244140625.
- Multiply 244140625 by 25 to get 6103515625.
- Multiply 6103515625 by 25 to get 152587890625.
- Multiply 152587890625 by 25 to get 3814697265625.
- The final result is 3814697265625.
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 "25 to the power of 9" mean?
25 to the power of 9" (25^9) is a mathematical expression that signifies multiplying the base number, 25, by itself three times. It's equivalent to 25 x 25 x 25, which equals 3814697265625.
How is "25 to the power of 9" calculated?
Calculating 25^9 is done by multiplying 25 by itself three times. So, 25^9 = 25 x 25 x 25, resulting in 3814697265625.
Can I calculate "25 to the power of 9" with negative exponents?
Negative exponents indicate taking the reciprocal of the base raised to the positive exponent. For example, 25^(-9) is equivalent to 1 / (25^9), which is 1/3814697265625.
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 |