500 to the Power of 3 = 500 3 = 125000000
500 to the power of 3 = 125000000
Welcome to our exponent calculator! We're exploring the concept of "500 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, 500 is the base, and 3 is the exponent.
Calculation
To calculate 500 to the power of 3, we multiply 500 by itself 3 times. Here's the step-by-step process:
| Step | Calculation | Result |
|---|---|---|
| 1 | 500 | 500 |
| 2 | 500 × 500 | 250000 |
| 3 | 500 × 500 × 500 | 125000000 |
Solution: 500 to the power of 3 is equal to 125000000.
How to write 500 to the power of 3 ?
Step 1: Understand the Concept
"500 to the power of 3" means we're multiplying 500 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, 500 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 5003.
Step 4: Calculate the Result
If we actually compute this:
Practice
Try writing these on your own:
- 499 to the power of 2
- 501 to the power of 4
- 3 to the power of 500
Interactive Power Calculator
Similar Calculations:
| Number | Power | Answer |
|---|---|---|
| 501 | 3 | 5013 = 125751501 |
| 502 | 3 | 5023 = 126506008 |
| 503 | 3 | 5033 = 127263527 |
Related Mathematical Operations
Square Root
The square root is the inverse operation of squaring a number. For our example:
v127263527 ≈ 11,281.1137
This is approximate because 500^3 isn't a perfect square.
Logarithm
Logarithms are the inverse of exponential functions. The logarithm of 127263527 with base 500 should equal 3:
log500(127263527) = 3
Exponent Properties
1. Multiplying exponents with the same base: 500a * 500b = 500(a+b)
Example: 5002 * 5003 = 5005 = 31250000000000
2. Dividing exponents with the same base: 500a / 500b = 500(a-b)
Example: 5005 / 5002 = 5003 = 125000000