480 to the Power of 3 = 480 3 = 110592000
480 to the power of 3 = 110592000
Welcome to our exponent calculator! We're exploring the concept of "480 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, 480 is the base, and 3 is the exponent.
Calculation
To calculate 480 to the power of 3, we multiply 480 by itself 3 times. Here's the step-by-step process:
| Step | Calculation | Result |
|---|---|---|
| 1 | 480 | 480 |
| 2 | 480 × 480 | 230400 |
| 3 | 480 × 480 × 480 | 110592000 |
Solution: 480 to the power of 3 is equal to 110592000.
How to write 480 to the power of 3 ?
Step 1: Understand the Concept
"480 to the power of 3" means we're multiplying 480 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, 480 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 4803.
Step 4: Calculate the Result
If we actually compute this:
Practice
Try writing these on your own:
- 479 to the power of 2
- 481 to the power of 4
- 3 to the power of 480
Interactive Power Calculator
Similar Calculations:
| Number | Power | Answer |
|---|---|---|
| 481 | 3 | 4813 = 111284641 |
| 482 | 3 | 4823 = 111980168 |
| 483 | 3 | 4833 = 112678587 |
Related Mathematical Operations
Square Root
The square root is the inverse operation of squaring a number. For our example:
v112678587 ≈ 10,615.0171
This is approximate because 480^3 isn't a perfect square.
Logarithm
Logarithms are the inverse of exponential functions. The logarithm of 112678587 with base 480 should equal 3:
log480(112678587) = 3
Exponent Properties
1. Multiplying exponents with the same base: 480a * 480b = 480(a+b)
Example: 4802 * 4803 = 4805 = 25480396800000
2. Dividing exponents with the same base: 480a / 480b = 480(a-b)
Example: 4805 / 4802 = 4803 = 110592000