Introduction to Fraction Exponent Calculator:
Fraction Exponent Calculator is a great source of finding fraction exponential problems. If you do complex calculations manually it takes time and effort to solving fractional exponents questions and if any error is found then you have to start the process and calculations again.
To avoid all the trouble we introduce our fractional exponents solver which is a helpful tool for anyone who is dealing with the calculations of cube roots, square roots, and powers with fractional exponents. It simplifies complex calculations and provides accurate results in a few seconds.
What is Fraction Exponent?
Fractional exponents are that fractions which became the power of an exponential function. It is also known as rational exponents, in which the power or root of a number is expressed as a fraction as xm/n. Here nth root of x is raised to the power of m/n.
This method is used to calculate the square roots, cube roots, or higher roots of numbers and simplify the given expressions. For example, x½ represents the square root of x in which ½ is the fraction part and x behaves as an exponential function.
How to Calculate Fraction Exponents?
For the calculation of complex and lengthy problems of fractional exponents, you need to focus on some important points suggested by the fraction exponent calculator that will help you to easily calculate the fraction exponent problems. These important points are:
Step 1:
A fraction exponent is represented in the fraction exponents calculator as xm/n, where x is the base, and ๐/๐ is the fractional exponent. x can represent either a power or a root, depending on whether ๐/๐ is positive or negative and where n is odd or even.
Step 2:
To evaluate ๐ฅm/n, the exponent fraction calculator follows some rules of exponents that are essential for calculation.
- Positive Exponent (m/n>0):
If n = 1, it represents a regular integer exponent, and you can calculate it directly. However, if n > 1, it represents a root. Then calculate the nth root of x and raise it to the power of m.
For example, fraction exponent ๐ฅ2/3, calculate the cube root of x and then raise it to the power of 2.
- Negative Exponent (m/n < 0):
It represents the reciprocal of a power or root with a positive exponent. After that calculate the positive exponent first and then take the reciprocal.
For example ๐ฅ−2/3, first calculate ๐ฅโ and then take its reciprocal.
Step 3:
After following step 2, use some rules of exponents.
- Product Rule:
$$ ๐ฅ^๐ \times ๐ฅ^๐ \;=\; ๐ฅ^(๐+๐) $$
- Quotient Rule:
$$ ๐ฅ^{\frac{๐}{๐ฅ^๐}} \;=\; ๐ฅ^{๐−๐} $$
- Power Rule:
$$ (๐ฅ^๐)๐ \;=\; ๐ฅ^{๐๐} $$
- Root Rule:
$$ ๐ฅ^1 ๐ \;=\; ๐ฅ^๐ $$
Step 4:
Lastly, apply the appropriate rule based on the value of the exponent (๐/๐) for finding the root number values.
This is the procedure followed by the fractional exponent calculator for solving fractional exponents problems for finding roots, despite you can get a better understanding with the help of the given example.
Solved Example of Fraction Exponent:
The fraction exponent calculator can help you to solve various exponent fractions but it crucial to know the manual calculations so an example is given below,
Example:
Solve the following:
$$ x^{\frac{4}{3}} \;=\; 81 $$
Solution:
$$ (x^{\frac{4}{3}})^{\frac{3}{4}} \;=\; \pm 81^{\frac{3}{4}} $$
$$ x \;=\; \pm (\sqrt[4]{81})^3 $$
$$ x \;=\; \pm (3)^3 $$
$$ x \;=\; \pm 27 $$
Example:
Evaluate the following:
$$ 8^{\frac{2}{3}} $$
Solution:
$$ 8^{\frac{2}{3}} \;=\; (8^2)^{\frac{1}{3}} $$
$$ =\; (8^{\frac{1}{3}} )^2 $$
$$ \biggr( 8^{\frac{1}{3}} \biggr)^2 \;=\; (2)^2 \;=\; 4 $$
How to Use Fraction Exponent Calculator?
The fractional exponents solver has a user-friendly interface, that allows you to use it to calculate fractional exponent questions.
Before adding the input in the form of number value for different types of numbers in the fraction exponents calculator, you must follow some simple instructions to avoid trouble. These instructions are:
- Enter the first number in the input box.
- Enter the second number in the next input box.
- Review your input number value before hitting the calculate button to start the calculation process in the fraction with exponent calculator.
- Click on the “Calculate” button to get the desired result of your given long multiplication problem.
- If you want to try out our fractional exponents calculator first then you can use the load example for a better understanding.
- Click on the “Recalculate” button to get a new page for solving fractional exponents and more number values of multiplication.
Output of Fractional Exponents Solver:
The fraction exponent Calculator gives you the solution to a given number problem when you add the input to it. It provides you with solutions to Fraction exponent problems in a step-wise process. It may contain as:
- Result Option:
You can click on the result option and it provides you with a solution for finding the root of different numbers.
- Possible Step:
When you click on the possible steps option it provides you with the solution of fraction exponent questions where all calculation steps are included in detail.
Advantages of Fraction Exponents Calculator:
The fractions calculator with exponents gives you millions of advantages whenever you use it to calculate root number value problems to get the solution. These advantages are:
- Our exponent fraction calculator saves the time that you consume in doing complex calculations of the Fraction exponent question and provides solutions in a few seconds.
- It is a free-of-cost tool so you can use it to find the root number for cube, square or even power for different numbers with the solution without paying anything.
- The fractional exponent calculator is an adaptive tool that allows you to solve various types of root questions in an easy way.
- You can use this fractional exponents solver for practice so that you get a strong hold on the fraction exponent concept.
- The fractional exponents calculator is a trustworthy tool that provides exact solutions as per your input root value whenever you use it to calculate the Fraction exponent problem.
- The fraction exponent calculator provides you solution of fraction exponent with a complete process in a step-by-step method so that you get more clarity.
