164 to the Power of 3 = 164 3 = 4410944
Welcome to our exponent calculator! We're exploring the concept of "164 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, 164 is the base, and 3 is the exponent.
Calculation
To calculate 164 to the power of 3, we multiply 164 by itself 3 times. Here's the step-by-step process:
| Step | Calculation | Result |
|---|---|---|
| 1 | 164 | 164 |
| 2 | 164 × 164 | 26896 |
| 3 | 164 × 164 × 164 | 4410944 |
Solution: 164 to the power of 3 is equal to 4410944.
How to write 164 to the power of 3 ?
Step 1: Understand the Concept
"164 to the power of 3" means we're multiplying 164 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, 164 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 1643.
Step 4: Calculate the Result
If we actually compute this:
Practice
Try writing these on your own:
- 163 to the power of 2
- 165 to the power of 4
- 3 to the power of 164
Interactive Power Calculator
Similar Calculations:
| Number | Power | Answer |
|---|---|---|
| 165 | 3 | 1653 = 4492125 |
| 166 | 3 | 1663 = 4574296 |
| 167 | 3 | 1673 = 4657463 |
Related Mathematical Operations
Square Root
The square root is the inverse operation of squaring a number. For our example:
v4657463 ≈ 2,158.1156
This is approximate because 164^3 isn't a perfect square.
Logarithm
Logarithms are the inverse of exponential functions. The logarithm of 4657463 with base 164 should equal 3:
log164(4657463) = 3
Exponent Properties
1. Multiplying exponents with the same base: 164a * 164b = 164(a+b)
Example: 1642 * 1643 = 1645 = 118636749824
2. Dividing exponents with the same base: 164a / 164b = 164(a-b)
Example: 1645 / 1642 = 1643 = 4410944