270 to the Power of 3 = 270 3 = 19683000
Welcome to our exponent calculator! We're exploring the concept of "270 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, 270 is the base, and 3 is the exponent.
Calculation
To calculate 270 to the power of 3, we multiply 270 by itself 3 times. Here's the step-by-step process:
| Step | Calculation | Result |
|---|---|---|
| 1 | 270 | 270 |
| 2 | 270 × 270 | 72900 |
| 3 | 270 × 270 × 270 | 19683000 |
Solution: 270 to the power of 3 is equal to 19683000.
How to write 270 to the power of 3 ?
Step 1: Understand the Concept
"270 to the power of 3" means we're multiplying 270 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, 270 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 2703.
Step 4: Calculate the Result
If we actually compute this:
Practice
Try writing these on your own:
- 269 to the power of 2
- 271 to the power of 4
- 3 to the power of 270
Interactive Power Calculator
Similar Calculations:
| Number | Power | Answer |
|---|---|---|
| 271 | 3 | 2713 = 19902511 |
| 272 | 3 | 2723 = 20123648 |
| 273 | 3 | 2733 = 20346417 |
Related Mathematical Operations
Square Root
The square root is the inverse operation of squaring a number. For our example:
v20346417 ≈ 4,510.7003
This is approximate because 270^3 isn't a perfect square.
Logarithm
Logarithms are the inverse of exponential functions. The logarithm of 20346417 with base 270 should equal 3:
log270(20346417) = 3
Exponent Properties
1. Multiplying exponents with the same base: 270a * 270b = 270(a+b)
Example: 2702 * 2703 = 2705 = 1434890700000
2. Dividing exponents with the same base: 270a / 270b = 270(a-b)
Example: 2705 / 2702 = 2703 = 19683000