216 to the Power of 3 = 216 3 = 10077696
Welcome to our exponent calculator! We're exploring the concept of "216 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, 216 is the base, and 3 is the exponent.
Calculation
To calculate 216 to the power of 3, we multiply 216 by itself 3 times. Here's the step-by-step process:
| Step | Calculation | Result |
|---|---|---|
| 1 | 216 | 216 |
| 2 | 216 × 216 | 46656 |
| 3 | 216 × 216 × 216 | 10077696 |
Solution: 216 to the power of 3 is equal to 10077696.
How to write 216 to the power of 3 ?
Step 1: Understand the Concept
"216 to the power of 3" means we're multiplying 216 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, 216 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 2163.
Step 4: Calculate the Result
If we actually compute this:
Practice
Try writing these on your own:
- 215 to the power of 2
- 217 to the power of 4
- 3 to the power of 216
Interactive Power Calculator
Similar Calculations:
| Number | Power | Answer |
|---|---|---|
| 217 | 3 | 2173 = 10218313 |
| 218 | 3 | 2183 = 10360232 |
| 219 | 3 | 2193 = 10503459 |
Related Mathematical Operations
Square Root
The square root is the inverse operation of squaring a number. For our example:
v10503459 ≈ 3,240.9040
This is approximate because 216^3 isn't a perfect square.
Logarithm
Logarithms are the inverse of exponential functions. The logarithm of 10503459 with base 216 should equal 3:
log216(10503459) = 3
Exponent Properties
1. Multiplying exponents with the same base: 216a * 216b = 216(a+b)
Example: 2162 * 2163 = 2165 = 470184984576
2. Dividing exponents with the same base: 216a / 216b = 216(a-b)
Example: 2165 / 2162 = 2163 = 10077696