169 to the Power of 5 = 169 5 = 137858491849
Welcome to our exponent calculator! We're exploring the concept of "169 to the power of 5". 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, 169 is the base, and 5 is the exponent.
Calculation
To calculate 169 to the power of 5, we multiply 169 by itself 5 times. Here's the step-by-step process:
| Step | Calculation | Result |
|---|---|---|
| 1 | 169 | 169 |
| 2 | 169 × 169 | 28561 |
| 3 | 169 × 169 × 169 | 4826809 |
| 4 | 169 × 169 × 169 × 169 | 815730721 |
| 5 | 169 × 169 × 169 × 169 × 169 | 137858491849 |
Solution: 169 to the power of 5 is equal to 137858491849.
How to write 169 to the power of 5 ?
Step 1: Understand the Concept
"169 to the power of 5" means we're multiplying 169 by itself 5 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, 169 is called the "base", and 5 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 1695.
Step 4: Calculate the Result
If we actually compute this:
Practice
Try writing these on your own:
- 168 to the power of 4
- 170 to the power of 6
- 5 to the power of 169
Interactive Power Calculator
Similar Calculations:
| Number | Power | Answer |
|---|---|---|
| 170 | 5 | 1705 = 141985700000 |
| 171 | 5 | 1715 = 146211169851 |
| 172 | 5 | 1725 = 150536645632 |
| 169 | 4 | 1694 = 815730721 |
Related Mathematical Operations
Square Root
The square root is the inverse operation of squaring a number. For our example:
v815730721 ≈ 28,561.0000
This is approximate because 169^5 isn't a perfect square.
Logarithm
Logarithms are the inverse of exponential functions. The logarithm of 815730721 with base 169 should equal 5:
log169(815730721) = 5
Exponent Properties
1. Multiplying exponents with the same base: 169a * 169b = 169(a+b)
Example: 1692 * 1693 = 1695 = 137858491849
2. Dividing exponents with the same base: 169a / 169b = 169(a-b)
Example: 1695 / 1692 = 1693 = 4826809