264 to the Power of 3 = 264 3 = 18399744
264 to the power of 3 = 18399744
Welcome to our exponent calculator! We're exploring the concept of "264 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, 264 is the base, and 3 is the exponent.
Calculation
To calculate 264 to the power of 3, we multiply 264 by itself 3 times. Here's the step-by-step process:
| Step | Calculation | Result |
|---|---|---|
| 1 | 264 | 264 |
| 2 | 264 × 264 | 69696 |
| 3 | 264 × 264 × 264 | 18399744 |
Solution: 264 to the power of 3 is equal to 18399744.
How to write 264 to the power of 3 ?
Step 1: Understand the Concept
"264 to the power of 3" means we're multiplying 264 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, 264 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 2643.
Step 4: Calculate the Result
If we actually compute this:
Practice
Try writing these on your own:
- 263 to the power of 2
- 265 to the power of 4
- 3 to the power of 264
Interactive Power Calculator
Similar Calculations:
| Number | Power | Answer |
|---|---|---|
| 265 | 3 | 2653 = 18609625 |
| 266 | 3 | 2663 = 18821096 |
| 267 | 3 | 2673 = 19034163 |
Related Mathematical Operations
Square Root
The square root is the inverse operation of squaring a number. For our example:
v19034163 ≈ 4,362.8159
This is approximate because 264^3 isn't a perfect square.
Logarithm
Logarithms are the inverse of exponential functions. The logarithm of 19034163 with base 264 should equal 3:
log264(19034163) = 3
Exponent Properties
1. Multiplying exponents with the same base: 264a * 264b = 264(a+b)
Example: 2642 * 2643 = 2645 = 1282388557824
2. Dividing exponents with the same base: 264a / 264b = 264(a-b)
Example: 2645 / 2642 = 2643 = 18399744