200 to the Power of 3 = 200 3 = 8000000
Welcome to our exponent calculator! We're exploring the concept of "200 to the power of 3". Let's break down what this means and how to calculate it.
What are Exponents?
An exponent is a mathematical operation where we multiply a number (called the base) by itself a certain number of times (indicated by the power or exponent). In our case, 200 is the base, and 3 is the exponent.
Calculation
To calculate 200 to the power of 3, we multiply 200 by itself 3 times. Here's the step-by-step process:
| Step | Calculation | Result |
|---|---|---|
| 1 | 200 | 200 |
| 2 | 200 × 200 | 40000 |
| 3 | 200 × 200 × 200 | 8000000 |
Solution: 200 to the power of 3 is equal to 8000000.
How to write 200 to the power of 3 ?
Step 1: Understand the Concept
"200 to the power of 3" means we're multiplying 200 by itself 3 times. Let's break this down:
Step 2: Learn the Notation
In mathematics, we have a special way to write this more concisely. We use superscript notation:
Here, 200 is called the "base", and 3 is called the "exponent" or "power".
Step 3: Understand Alternative Notations
Sometimes, especially when typing or in programming, you might see it written as:
This means the same thing as 2003.
Step 4: Calculate the Result
If we actually compute this:
Practice
Try writing these on your own:
- 199 to the power of 2
- 201 to the power of 4
- 3 to the power of 200
Interactive Power Calculator
Similar Calculations:
| Number | Power | Answer |
|---|---|---|
| 201 | 3 | 2013 = 8120601 |
| 202 | 3 | 2023 = 8242408 |
| 203 | 3 | 2033 = 8365427 |
Related Mathematical Operations
Square Root
The square root is the inverse operation of squaring a number. For our example:
v8365427 ≈ 2,892.3048
This is approximate because 200^3 isn't a perfect square.
Logarithm
Logarithms are the inverse of exponential functions. The logarithm of 8365427 with base 200 should equal 3:
log200(8365427) = 3
Exponent Properties
1. Multiplying exponents with the same base: 200a * 200b = 200(a+b)
Example: 2002 * 2003 = 2005 = 320000000000
2. Dividing exponents with the same base: 200a / 200b = 200(a-b)
Example: 2005 / 2002 = 2003 = 8000000