402 to the Power of 3 = 402 3 = 64964808
Welcome to our exponent calculator! We're exploring the concept of "402 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, 402 is the base, and 3 is the exponent.
Calculation
To calculate 402 to the power of 3, we multiply 402 by itself 3 times. Here's the step-by-step process:
| Step | Calculation | Result |
|---|---|---|
| 1 | 402 | 402 |
| 2 | 402 × 402 | 161604 |
| 3 | 402 × 402 × 402 | 64964808 |
Solution: 402 to the power of 3 is equal to 64964808.
How to write 402 to the power of 3 ?
Step 1: Understand the Concept
"402 to the power of 3" means we're multiplying 402 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, 402 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 4023.
Step 4: Calculate the Result
If we actually compute this:
Practice
Try writing these on your own:
- 401 to the power of 2
- 403 to the power of 4
- 3 to the power of 402
Interactive Power Calculator
Similar Calculations:
| Number | Power | Answer |
|---|---|---|
| 403 | 3 | 4033 = 65450827 |
| 404 | 3 | 4043 = 65939264 |
| 405 | 3 | 4053 = 66430125 |
Related Mathematical Operations
Square Root
The square root is the inverse operation of squaring a number. For our example:
v66430125 ≈ 8,150.4678
This is approximate because 402^3 isn't a perfect square.
Logarithm
Logarithms are the inverse of exponential functions. The logarithm of 66430125 with base 402 should equal 3:
log402(66430125) = 3
Exponent Properties
1. Multiplying exponents with the same base: 402a * 402b = 402(a+b)
Example: 4022 * 4023 = 4025 = 10498572832032
2. Dividing exponents with the same base: 402a / 402b = 402(a-b)
Example: 4025 / 4022 = 4023 = 64964808