464 to the Power of 3 = 464 3 = 99897344
464 to the power of 3 = 99897344
Welcome to our exponent calculator! We're exploring the concept of "464 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, 464 is the base, and 3 is the exponent.
Calculation
To calculate 464 to the power of 3, we multiply 464 by itself 3 times. Here's the step-by-step process:
| Step | Calculation | Result |
|---|---|---|
| 1 | 464 | 464 |
| 2 | 464 × 464 | 215296 |
| 3 | 464 × 464 × 464 | 99897344 |
Solution: 464 to the power of 3 is equal to 99897344.
How to write 464 to the power of 3 ?
Step 1: Understand the Concept
"464 to the power of 3" means we're multiplying 464 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, 464 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 4643.
Step 4: Calculate the Result
If we actually compute this:
Practice
Try writing these on your own:
- 463 to the power of 2
- 465 to the power of 4
- 3 to the power of 464
Interactive Power Calculator
Similar Calculations:
| Number | Power | Answer |
|---|---|---|
| 465 | 3 | 4653 = 100544625 |
| 466 | 3 | 4663 = 101194696 |
| 467 | 3 | 4673 = 101847563 |
Related Mathematical Operations
Square Root
The square root is the inverse operation of squaring a number. For our example:
v101847563 ≈ 10,091.9554
This is approximate because 464^3 isn't a perfect square.
Logarithm
Logarithms are the inverse of exponential functions. The logarithm of 101847563 with base 464 should equal 3:
log464(101847563) = 3
Exponent Properties
1. Multiplying exponents with the same base: 464a * 464b = 464(a+b)
Example: 4642 * 4643 = 4645 = 21507498573824
2. Dividing exponents with the same base: 464a / 464b = 464(a-b)
Example: 4645 / 4642 = 4643 = 99897344