What is 3 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 "3 to the power of 10." We'll break down the concept, explain the calculation method, and discuss the significance of this mathematical operation.
Answer: 3 to the Power of 10 is 59049
Step 1: Understanding Exponents
Step 2: The Calculation Process
Calculating 3^10 is straightforward. Follow these steps:
- Start with 3 to the power of 10.
- Multiply 1 by 3 to get 3.
- Multiply 3 by 3 to get 9.
- Multiply 9 by 3 to get 27.
- Multiply 27 by 3 to get 81.
- Multiply 81 by 3 to get 243.
- Multiply 243 by 3 to get 729.
- Multiply 729 by 3 to get 2187.
- Multiply 2187 by 3 to get 6561.
- Multiply 6561 by 3 to get 19683.
- Multiply 19683 by 3 to get 59049.
- The final result is 59049.
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 "3 to the power of 10" mean?
3 to the power of 10" (3^10) is a mathematical expression that signifies multiplying the base number, 3, by itself three times. It's equivalent to 3 x 3 x 3, which equals 59049.
How is "3 to the power of 10" calculated?
Calculating 3^10 is done by multiplying 3 by itself three times. So, 3^10 = 3 x 3 x 3, resulting in 59049.
Can I calculate "3 to the power of 10" with negative exponents?
Negative exponents indicate taking the reciprocal of the base raised to the positive exponent. For example, 3^(-10) is equivalent to 1 / (3^10), which is 1/59049.
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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