489 to the Power of 3 = 489 3 = 116930169
489 to the power of 3 = 116930169
Welcome to our exponent calculator! We're exploring the concept of "489 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, 489 is the base, and 3 is the exponent.
Calculation
To calculate 489 to the power of 3, we multiply 489 by itself 3 times. Here's the step-by-step process:
| Step | Calculation | Result |
|---|---|---|
| 1 | 489 | 489 |
| 2 | 489 × 489 | 239121 |
| 3 | 489 × 489 × 489 | 116930169 |
Solution: 489 to the power of 3 is equal to 116930169.
How to write 489 to the power of 3 ?
Step 1: Understand the Concept
"489 to the power of 3" means we're multiplying 489 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, 489 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 4893.
Step 4: Calculate the Result
If we actually compute this:
Practice
Try writing these on your own:
- 488 to the power of 2
- 490 to the power of 4
- 3 to the power of 489
Interactive Power Calculator
Similar Calculations:
| Number | Power | Answer |
|---|---|---|
| 490 | 3 | 4903 = 117649000 |
| 491 | 3 | 4913 = 118370771 |
| 492 | 3 | 4923 = 119095488 |
Related Mathematical Operations
Square Root
The square root is the inverse operation of squaring a number. For our example:
v119095488 ≈ 10,913.0879
This is approximate because 489^3 isn't a perfect square.
Logarithm
Logarithms are the inverse of exponential functions. The logarithm of 119095488 with base 489 should equal 3:
log489(119095488) = 3
Exponent Properties
1. Multiplying exponents with the same base: 489a * 489b = 489(a+b)
Example: 4892 * 4893 = 4895 = 27960458941449
2. Dividing exponents with the same base: 489a / 489b = 489(a-b)
Example: 4895 / 4892 = 4893 = 116930169