Introduction to Modular Exponentiation Calculator:
Modular exponentiation calculator is an online tool that is used to find the exponential power mod value of a given function value. It helps you to simplify the process of finding the large and complex mod value quotient value.
Our power mod calculator with steps can handle different types of large exponentiation problems solution without any trouble. You can just give the input value in it and get a solution immediately.
What is a Power Mod?
Power Mod is the combination of exponential and modular arithmetic which is used to find the exponential power of the mod of a given expression. It is a complex method because it is the concept for higher-order mathematics.
A power mod is used in various fields, including mathematics, engineering, and game design, to compute the power mod number that is raised to a certain power and to find the result of the modulo in a specific number.
Formula of Power Mod:
The formula of power mod consists of a base and the exponential power of a particular number. The formula behind the modular exponentiation calculator is given below,
$$ x^y \; mod\; n \;=\; ? $$
Whereas,
- x is the base of exponential power.
- y is the exponential power of the base x.
- n is the number that divides the exponential power number.
How to Calculate the Power Mod?
The mod calculator with exponents calculates the exponential power of modulo with the help of a binary operation system by using some simple steps. These steps are:
Step 1:
Identify the given value of the exponential power mod and n number that divide the modular.
Step 2:
Before starting the iteration, the modulo exponentiation calculator check the exponential power if it is even and odd. You should also check it before calculation. If it is odd then we make it a power the given odd power for solution because the power doubles in even exponential power.
Step 3:
By power mod formula,
$$ x^y \;mod\; n \;=\; ? $$
Start putting iteration in which the y value varies till the required exponential that is given in the question is not achieved as y = 1, 2, 4, 8, 16, 32, 64,...
Step 4:
After finding the required modular number you need to multiply all the above iteration results that you get from the power mod formula.
Step 5:
Lastly, take the mod of multiple number results with a given modular number to get the result of the power mod question easily.
Although it is a difficult concept you need to follow the above steps to get a solution. You can look at the below example that will clear all your doubts.
Solved Example of Power Mod:
A solved example of a power mod question gives you a clear understanding about the working process of exponent modulo calculator.
Example:
Calculate the following:
$$ 3^{15}\; mod\;10 $$
Solution:
The given exponential mod power is 315 and the divisor value which is 10 number.
$$ 3^1 \;mod\; 10 \;=\; 3 \;≡\; mod\; 10 \;=\; 3 $$
$$ 3^2\; mod\; 10 \;=\; 3^2 \;≡\; mod\; 10 \;=\; 9 $$
$$ 3^4\; mod\; 10 \;=\; 3^4 \;≡\; mod\; 10 \;=\; 81 \;≡\; mod\; 10 \;=\; 1 $$
$$ 3^8\; mod\; 10 \;=\; 3^8 \;≡\; mod\; 10 \;=\; 3^4. 3^4 \;≡\; mode\; 10 \;=1.1.1 $$
$$ 3^15\; mod\; 10 \;=\; (3^1\; mod\; 10. 3^2 \;mod\; 10. 3^4\; mod\; 10. 3^8 \;mod\; 10) $$
$$ 3^15\; mod\; 10\; =\; (3.9.1.1) $$
$$ 3^15\; mod\; 10 \;=\; 27 $$
$$ 27\; mod\; 10 \;=\; 7 $$
How to Use Modular Exponentiation Calculator?
Power mod calculator with steps has a simple design that helps everyone to solve the given power mod question immediately. You just need to put your power mod problem in it and follow some important instructions to get results. These instructions are:
- Enter the value of the base of the power mod problem in the input field.
- Enter the value of the exponential power of the base for the power mod problem in the input field.
- Enter the value of the divisor number for the power mod problem in the input field.
- Review your given input value to get the exact solution to the power mod question.
- The calculate button evaluates the power mod problem in the mod calculator with exponents.
- If you want to check the modulo exponent calculator then you can use the load example and get its solution to know more about this concept.
- Click the “Recalculate” button for the evaluation of more examples of the power mod with the solution.
Final Result of Power Mod Calculator:
Modular exponentiation calculator provides you with a solution as per your input problem when you click on the calculate button. It may contain as:
In the Result Box:
Click on the result button so that you get the solution of the power mod problem.
Steps Box:
When you click on the steps option of the mod exponent calculator, you get the solution to power mod questions in a stepwise process.
Benefits of Using Mod Calculator with Exponents:
The exponent modulo calculator has many benefits that you obtain when you use it to solve power modular value problems to get its solution. Our tool takes the input of power mod and provides a solution without putting any condition on signup. These benefits are,
- Modulo exponentiation calculator is a reliable tool as it always provides you with accurate solutions for the given exponential power modular.
- It is a speedy tool that provides solutions exponential mod problem with solution in a few seconds.
- Powermod calculator is a learning tool that helps parents teach their children about the concept of power mod very easily through online platforms.
- It is a handy tool that solves power mod problems quickly and you do not put any type of external effort.
- Mod exponent calculator is a free tool that allows you to use it for the calculation of power mod problems without taking a fee.
- Modular exponentiation calculator is an easy-to-use tool, anyone or even a beginner can easily use it for the solution of power mod problems.
