13 to the Power of 8 = 13 8 = 815730721
13 to the power of 8 = 815730721
Welcome to our exponent calculator! We're exploring the concept of "13 to the power of 8". 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, 13 is the base, and 8 is the exponent.
Calculation
To calculate 13 to the power of 8, we multiply 13 by itself 8 times. Here's the step-by-step process:
| Step | Calculation | Result |
|---|---|---|
| 1 | 13 | 13 |
| 2 | 13 × 13 | 169 |
| 3 | 13 × 13 × 13 | 2197 |
| 4 | 13 × 13 × 13 × 13 | 28561 |
| 5 | 13 × 13 × 13 × 13 × 13 | 371293 |
| 6 | 13 × 13 × 13 × 13 × 13 × 13 | 4826809 |
| 7 | 13 × 13 × 13 × 13 × 13 × 13 × 13 | 62748517 |
| 8 | 13 × 13 × 13 × 13 × 13 × 13 × 13 × 13 | 815730721 |
Solution: 13 to the power of 8 is equal to 815730721.
How to write 13 to the power of 8 ?
Step 1: Understand the Concept
"13 to the power of 8" means we're multiplying 13 by itself 8 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, 13 is called the "base", and 8 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 138.
Step 4: Calculate the Result
If we actually compute this:
Practice
Try writing these on your own:
- 12 to the power of 7
- 14 to the power of 9
- 8 to the power of 13
Interactive Power Calculator
Similar Calculations:
| Number | Power | Answer |
|---|---|---|
| 14 | 8 | 148 = 1475789056 |
| 15 | 8 | 158 = 2562890625 |
| 16 | 8 | 168 = 4294967296 |
| 13 | 7 | 137 = 62748517 |
Related Mathematical Operations
Square Root
The square root is the inverse operation of squaring a number. For our example:
v62748517 ≈ 7,921.3962
This is approximate because 13^8 isn't a perfect square.
Logarithm
Logarithms are the inverse of exponential functions. The logarithm of 62748517 with base 13 should equal 8:
log13(62748517) = 8
Exponent Properties
1. Multiplying exponents with the same base: 13a * 13b = 13(a+b)
Example: 132 * 133 = 135 = 371293
2. Dividing exponents with the same base: 13a / 13b = 13(a-b)
Example: 135 / 132 = 133 = 2197