What is 3 to the Power of 8? 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 8." We'll break down the concept, explain the calculation method, and discuss the significance of this mathematical operation.
Answer: 3 to the Power of 8 is 6561
Step 1: Understanding Exponents
Step 2: The Calculation Process
Calculating 3^8 is straightforward. Follow these steps:
- Start with 3 to the power of 8.
- 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.
- The final result is 6561.
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 8" mean?
3 to the power of 8" (3^8) 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 6561.
How is "3 to the power of 8" calculated?
Calculating 3^8 is done by multiplying 3 by itself three times. So, 3^8 = 3 x 3 x 3, resulting in 6561.
Can I calculate "3 to the power of 8" with negative exponents?
Negative exponents indicate taking the reciprocal of the base raised to the positive exponent. For example, 3^(-8) is equivalent to 1 / (3^8), which is 1/6561.
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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