105 to the Power of 4 = 105 4 = 121550625
Welcome to our exponent calculator! We're exploring the concept of "105 to the power of 4". 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, 105 is the base, and 4 is the exponent.
Calculation
To calculate 105 to the power of 4, we multiply 105 by itself 4 times. Here's the step-by-step process:
| Step | Calculation | Result |
|---|---|---|
| 1 | 105 | 105 |
| 2 | 105 × 105 | 11025 |
| 3 | 105 × 105 × 105 | 1157625 |
| 4 | 105 × 105 × 105 × 105 | 121550625 |
Solution: 105 to the power of 4 is equal to 121550625.
How to write 105 to the power of 4 ?
Step 1: Understand the Concept
"105 to the power of 4" means we're multiplying 105 by itself 4 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, 105 is called the "base", and 4 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 1054.
Step 4: Calculate the Result
If we actually compute this:
Practice
Try writing these on your own:
- 104 to the power of 3
- 106 to the power of 5
- 4 to the power of 105
Interactive Power Calculator
Similar Calculations:
| Number | Power | Answer |
|---|---|---|
| 106 | 4 | 1064 = 126247696 |
| 107 | 4 | 1074 = 131079601 |
| 108 | 4 | 1084 = 136048896 |
| 105 | 3 | 1053 = 1157625 |
Related Mathematical Operations
Square Root
The square root is the inverse operation of squaring a number. For our example:
v1157625 ≈ 1,075.9298
This is approximate because 105^4 isn't a perfect square.
Logarithm
Logarithms are the inverse of exponential functions. The logarithm of 1157625 with base 105 should equal 4:
log105(1157625) = 4
Exponent Properties
1. Multiplying exponents with the same base: 105a * 105b = 105(a+b)
Example: 1052 * 1053 = 1055 = 12762815625
2. Dividing exponents with the same base: 105a / 105b = 105(a-b)
Example: 1055 / 1052 = 1053 = 1157625