240 to the Power of 3 = 240 3 = 13824000
Welcome to our exponent calculator! We're exploring the concept of "240 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, 240 is the base, and 3 is the exponent.
Calculation
To calculate 240 to the power of 3, we multiply 240 by itself 3 times. Here's the step-by-step process:
| Step | Calculation | Result |
|---|---|---|
| 1 | 240 | 240 |
| 2 | 240 × 240 | 57600 |
| 3 | 240 × 240 × 240 | 13824000 |
Solution: 240 to the power of 3 is equal to 13824000.
How to write 240 to the power of 3 ?
Step 1: Understand the Concept
"240 to the power of 3" means we're multiplying 240 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, 240 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 2403.
Step 4: Calculate the Result
If we actually compute this:
Practice
Try writing these on your own:
- 239 to the power of 2
- 241 to the power of 4
- 3 to the power of 240
Interactive Power Calculator
Similar Calculations:
| Number | Power | Answer |
|---|---|---|
| 241 | 3 | 2413 = 13997521 |
| 242 | 3 | 2423 = 14172488 |
| 243 | 3 | 2433 = 14348907 |
Related Mathematical Operations
Square Root
The square root is the inverse operation of squaring a number. For our example:
v14348907 ≈ 3,787.9951
This is approximate because 240^3 isn't a perfect square.
Logarithm
Logarithms are the inverse of exponential functions. The logarithm of 14348907 with base 240 should equal 3:
log240(14348907) = 3
Exponent Properties
1. Multiplying exponents with the same base: 240a * 240b = 240(a+b)
Example: 2402 * 2403 = 2405 = 796262400000
2. Dividing exponents with the same base: 240a / 240b = 240(a-b)
Example: 2405 / 2402 = 2403 = 13824000