What is 2 to the Power of 17? 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 "2 to the power of 17." We'll break down the concept, explain the calculation method, and discuss the significance of this mathematical operation.
Answer: 2 to the Power of 17 is 131072
Step 1: Understanding Exponents
Step 2: The Calculation Process
Calculating 2^17 is straightforward. Follow these steps:
- Start with 2 to the power of 17.
- Multiply 1 by 2 to get 2.
- Multiply 2 by 2 to get 4.
- Multiply 4 by 2 to get 8.
- Multiply 8 by 2 to get 16.
- Multiply 16 by 2 to get 32.
- Multiply 32 by 2 to get 64.
- Multiply 64 by 2 to get 128.
- Multiply 128 by 2 to get 256.
- Multiply 256 by 2 to get 512.
- Multiply 512 by 2 to get 1024.
- Multiply 1024 by 2 to get 2048.
- Multiply 2048 by 2 to get 4096.
- Multiply 4096 by 2 to get 8192.
- Multiply 8192 by 2 to get 16384.
- Multiply 16384 by 2 to get 32768.
- Multiply 32768 by 2 to get 65536.
- Multiply 65536 by 2 to get 131072.
- The final result is 131072.
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 "2 to the power of 17" mean?
2 to the power of 17" (2^17) is a mathematical expression that signifies multiplying the base number, 2, by itself three times. It's equivalent to 2 x 2 x 2, which equals 131072.
How is "2 to the power of 17" calculated?
Calculating 2^17 is done by multiplying 2 by itself three times. So, 2^17 = 2 x 2 x 2, resulting in 131072.
Can I calculate "2 to the power of 17" with negative exponents?
Negative exponents indicate taking the reciprocal of the base raised to the positive exponent. For example, 2^(-17) is equivalent to 1 / (2^17), which is 1/131072.
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 |
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