475 to the Power of 3 = 475 3 = 107171875
475 to the power of 3 = 107171875
Welcome to our exponent calculator! We're exploring the concept of "475 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, 475 is the base, and 3 is the exponent.
Calculation
To calculate 475 to the power of 3, we multiply 475 by itself 3 times. Here's the step-by-step process:
| Step | Calculation | Result |
|---|---|---|
| 1 | 475 | 475 |
| 2 | 475 × 475 | 225625 |
| 3 | 475 × 475 × 475 | 107171875 |
Solution: 475 to the power of 3 is equal to 107171875.
How to write 475 to the power of 3 ?
Step 1: Understand the Concept
"475 to the power of 3" means we're multiplying 475 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, 475 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 4753.
Step 4: Calculate the Result
If we actually compute this:
Practice
Try writing these on your own:
- 474 to the power of 2
- 476 to the power of 4
- 3 to the power of 475
Interactive Power Calculator
Similar Calculations:
| Number | Power | Answer |
|---|---|---|
| 476 | 3 | 4763 = 107850176 |
| 477 | 3 | 4773 = 108531333 |
| 478 | 3 | 4783 = 109215352 |
Related Mathematical Operations
Square Root
The square root is the inverse operation of squaring a number. For our example:
v109215352 ≈ 10,450.6149
This is approximate because 475^3 isn't a perfect square.
Logarithm
Logarithms are the inverse of exponential functions. The logarithm of 109215352 with base 475 should equal 3:
log475(109215352) = 3
Exponent Properties
1. Multiplying exponents with the same base: 475a * 475b = 475(a+b)
Example: 4752 * 4753 = 4755 = 24180654296875
2. Dividing exponents with the same base: 475a / 475b = 475(a-b)
Example: 4755 / 4752 = 4753 = 107171875