490 to the Power of 3 = 490 3 = 117649000
490 to the power of 3 = 117649000
Welcome to our exponent calculator! We're exploring the concept of "490 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, 490 is the base, and 3 is the exponent.
Calculation
To calculate 490 to the power of 3, we multiply 490 by itself 3 times. Here's the step-by-step process:
| Step | Calculation | Result |
|---|---|---|
| 1 | 490 | 490 |
| 2 | 490 × 490 | 240100 |
| 3 | 490 × 490 × 490 | 117649000 |
Solution: 490 to the power of 3 is equal to 117649000.
How to write 490 to the power of 3 ?
Step 1: Understand the Concept
"490 to the power of 3" means we're multiplying 490 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, 490 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 4903.
Step 4: Calculate the Result
If we actually compute this:
Practice
Try writing these on your own:
- 489 to the power of 2
- 491 to the power of 4
- 3 to the power of 490
Interactive Power Calculator
Similar Calculations:
| Number | Power | Answer |
|---|---|---|
| 491 | 3 | 4913 = 118370771 |
| 492 | 3 | 4923 = 119095488 |
| 493 | 3 | 4933 = 119823157 |
Related Mathematical Operations
Square Root
The square root is the inverse operation of squaring a number. For our example:
v119823157 ≈ 10,946.3764
This is approximate because 490^3 isn't a perfect square.
Logarithm
Logarithms are the inverse of exponential functions. The logarithm of 119823157 with base 490 should equal 3:
log490(119823157) = 3
Exponent Properties
1. Multiplying exponents with the same base: 490a * 490b = 490(a+b)
Example: 4902 * 4903 = 4905 = 28247524900000
2. Dividing exponents with the same base: 490a / 490b = 490(a-b)
Example: 4905 / 4902 = 4903 = 117649000