428 to the Power of 3 = 428 3 = 78402752
428 to the power of 3 = 78402752
Welcome to our exponent calculator! We're exploring the concept of "428 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, 428 is the base, and 3 is the exponent.
Calculation
To calculate 428 to the power of 3, we multiply 428 by itself 3 times. Here's the step-by-step process:
| Step | Calculation | Result |
|---|---|---|
| 1 | 428 | 428 |
| 2 | 428 × 428 | 183184 |
| 3 | 428 × 428 × 428 | 78402752 |
Solution: 428 to the power of 3 is equal to 78402752.
How to write 428 to the power of 3 ?
Step 1: Understand the Concept
"428 to the power of 3" means we're multiplying 428 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, 428 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 4283.
Step 4: Calculate the Result
If we actually compute this:
Practice
Try writing these on your own:
- 427 to the power of 2
- 429 to the power of 4
- 3 to the power of 428
Interactive Power Calculator
Similar Calculations:
| Number | Power | Answer |
|---|---|---|
| 429 | 3 | 4293 = 78953589 |
| 430 | 3 | 4303 = 79507000 |
| 431 | 3 | 4313 = 80062991 |
Related Mathematical Operations
Square Root
The square root is the inverse operation of squaring a number. For our example:
v80062991 ≈ 8,947.7925
This is approximate because 428^3 isn't a perfect square.
Logarithm
Logarithms are the inverse of exponential functions. The logarithm of 80062991 with base 428 should equal 3:
log428(80062991) = 3
Exponent Properties
1. Multiplying exponents with the same base: 428a * 428b = 428(a+b)
Example: 4282 * 4283 = 4285 = 14362129722368
2. Dividing exponents with the same base: 428a / 428b = 428(a-b)
Example: 4285 / 4282 = 4283 = 78402752