467 to the Power of 3 = 467 3 = 101847563
467 to the power of 3 = 101847563
Welcome to our exponent calculator! We're exploring the concept of "467 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, 467 is the base, and 3 is the exponent.
Calculation
To calculate 467 to the power of 3, we multiply 467 by itself 3 times. Here's the step-by-step process:
| Step | Calculation | Result |
|---|---|---|
| 1 | 467 | 467 |
| 2 | 467 × 467 | 218089 |
| 3 | 467 × 467 × 467 | 101847563 |
Solution: 467 to the power of 3 is equal to 101847563.
How to write 467 to the power of 3 ?
Step 1: Understand the Concept
"467 to the power of 3" means we're multiplying 467 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, 467 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 4673.
Step 4: Calculate the Result
If we actually compute this:
Practice
Try writing these on your own:
- 466 to the power of 2
- 468 to the power of 4
- 3 to the power of 467
Interactive Power Calculator
Similar Calculations:
| Number | Power | Answer |
|---|---|---|
| 468 | 3 | 4683 = 102503232 |
| 469 | 3 | 4693 = 103161709 |
| 470 | 3 | 4703 = 103823000 |
Related Mathematical Operations
Square Root
The square root is the inverse operation of squaring a number. For our example:
v103823000 ≈ 10,189.3572
This is approximate because 467^3 isn't a perfect square.
Logarithm
Logarithms are the inverse of exponential functions. The logarithm of 103823000 with base 467 should equal 3:
log467(103823000) = 3
Exponent Properties
1. Multiplying exponents with the same base: 467a * 467b = 467(a+b)
Example: 4672 * 4673 = 4675 = 22211833167107
2. Dividing exponents with the same base: 467a / 467b = 467(a-b)
Example: 4675 / 4672 = 4673 = 101847563