349 to the Power of 3 = 349 3 = 42508549
Welcome to our exponent calculator! We're exploring the concept of "349 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, 349 is the base, and 3 is the exponent.
Calculation
To calculate 349 to the power of 3, we multiply 349 by itself 3 times. Here's the step-by-step process:
| Step | Calculation | Result |
|---|---|---|
| 1 | 349 | 349 |
| 2 | 349 × 349 | 121801 |
| 3 | 349 × 349 × 349 | 42508549 |
Solution: 349 to the power of 3 is equal to 42508549.
How to write 349 to the power of 3 ?
Step 1: Understand the Concept
"349 to the power of 3" means we're multiplying 349 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, 349 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 3493.
Step 4: Calculate the Result
If we actually compute this:
Practice
Try writing these on your own:
- 348 to the power of 2
- 350 to the power of 4
- 3 to the power of 349
Interactive Power Calculator
Similar Calculations:
| Number | Power | Answer |
|---|---|---|
| 350 | 3 | 3503 = 42875000 |
| 351 | 3 | 3513 = 43243551 |
| 352 | 3 | 3523 = 43614208 |
Related Mathematical Operations
Square Root
The square root is the inverse operation of squaring a number. For our example:
v43614208 ≈ 6,604.1054
This is approximate because 349^3 isn't a perfect square.
Logarithm
Logarithms are the inverse of exponential functions. The logarithm of 43614208 with base 349 should equal 3:
log349(43614208) = 3
Exponent Properties
1. Multiplying exponents with the same base: 349a * 349b = 349(a+b)
Example: 3492 * 3493 = 3495 = 5177583776749
2. Dividing exponents with the same base: 349a / 349b = 349(a-b)
Example: 3495 / 3492 = 3493 = 42508549