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# Fraction Exponent Calculator

$$x^\frac{n}{d}=\quad?$$

x (base):

n (numerator):

d (denominator):

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A fraction exponent calculator is designed to find the fractional exponent of a  number “X” of the form $$X^{\frac{n}{d}}$$. Where “X” is the base, the numerator of the exponent is “n” and the denominator is “d”.

## What is a Fractional Exponent?

“A Fractional Exponent can be defined as a number having power in terms of fraction rather than an integer.”

Where

X”, “n” and “d” = R

If we enter the other than the real number then we are not able to find the value of exponential fractions.

X(base)numerator/denominator = Xn/d

## How to Solve Fractions with Exponents?

There can be two situations we can face when solving the fractions with exponents. These can be multiplied by each other or divided.
We implement the two following laws of the exponents when solving the fractions with exponents:

• The Law of Multiplication of  Exponents
• The Law of Division of  Exponents

## The Law of Multiplication of  Exponents:

“ We need to add the exponents when multiplying the exponents.” This is the Law of the exponents for multiplication and we frequently apply it when simplifying fractional exponents in the multiplication of fractional exponents.

Let’s use the law of exponents for multiplication  which depicts  that we can add the exponents when multiplying two powers that have the same base:
x^a * x^b= x^(a+b)
Now consider how we can solve if n = 2
x * x=x¹ * x¹= x¹⁺¹=x²
Try this with any exponent number you like, it’s always true!

The fraction exponent calculator is compatible with multiplying Fractional Exponents.

## The Law of Division of  Exponents:

“Subtract  the exponents When we divide  the exponents.”

This is the Law of the exponents for division and we frequently apply it when simplifying fractional exponents in the division of fractional exponents.

Let’s use the law of exponents for the division  which describe subtracting the exponents when dividing  two powers that have the same base:
x^a/x^b= x^(a-b)
Now consider
x^2 / x=x^2 / x¹= x^2-1=x¹
Try this with any number you like, it’s always true!

The Fraction exponent calculator is suited to divide Fractional Exponents.

## Properties of the Fractional Exponents:

We need to simplify fractional exponents by knowing the properties of the fractional exponents.

### Fractional Exponents having Numerators “1”:

The fractional exponent is a way to express the power and base(roots) in one notation.

The fractional exponent having numerators are most commonly used in our calculation:

There are different kinds of Fractional Exponents having Numerators “1”:

• An exponent having an exponent like ½ (Square root exponent)
• An exponent having an exponent like 1/3 (Cube root exponent)
• An exponent having an exponent like 1/4 (Fourth root exponent)

We can portray the exponent as having a numerator like 1/k as follows:

X1/k= kx

The fraction exponent calculator is convenient to solve the exponents Fractional Exponents having  Numerators equal  “1”

Examples 1:

Now consider a fraction having an exponent (½)or

Then, let’s look at the fractional exponents of x:

x ^(1/2) * x ^(1/2)= ⎷x* ⎷x= x (1/2 + 1/2)= x¹=x

Convenient to use the square-root-calculator for solving the Square root, Fractional Exponents.

Examples 2:

Now consider a fraction having an exponent of cube root (1/3)or 3

Then, let’s look at the fractional exponents of x:

x (1/3) * x (1/3)* x (1/3)

= $$\sqrt[3]{}$$*$$\sqrt[3]{}$$* $$\sqrt[3]{}$$

=x (1/3 + 1/3+1/3)

= x¹

=x

### Fractional Exponents having Different  Numerators Than “1”:

How to solve fractions with exponents having different  numerators than “1”, in this condition the numerator of the fractions ≠ 1

Then our fraction with exponent should be like that:

Y=Xn(1/d)

Where:

n= Whole number the Fractional Exponents

1/d= A fractional part of the Fractional Exponents

X(n/d)

= X(n.1/d)

= (Xn)1/d

= (X1/d)n

X(n/d)= d⎷Xn=  [d⎷X]n

The fraction exponent calculator is easy to solve the exponent’s Fractional Exponents have Different  Numerators than “1”

Example:

Let’s try to understand where the base x = 4, fractional exponent = 3/2, the numerator part is 3 which is first solved then we solve the (½) the denominator part.

• 4 3/2 = 4 (3 * 1/2) = (43)1/2 = √(4³) = √64 = 8

Alternative Method:

• 4 3/2 = 4 (1/2) * 3 = (41/2)3 = (√4)³ = 2³ = 64

The fraction exponent calculator accepts the values of the Base, fractional parts of the numerator, and denominators separately.

### Fractional Exponents having Negative Fraction:

How to solve fractions with exponents having negative exponents. If our exponent is a negative number then how negative fraction exponents is going to be solved:

Consider:

X^-3

= 1/X+ 1/X+ 1/X+ 1/X

= 1/X3

We can represent it as:

X-n/d=[1/(d⎷Xn)]

The negative fractional exponents calculator is a convenient way to solve the negative fractional exponents.

## Working of the Fraction Exponent Calculator:

We do believe rational exponents calculator are straight forward, but just for the record we are going to explain the working of the calculator.

Input:

• Enter the values of the Base
• Enter the values of the numerator
• Enter the values of the denominator
• The calculate the fraction exponent

Output:

Fractional exponents calculator is an interesting way for students to find difficulty in how to solve fractions with exponents.

• The answer is given above
• All the steps involved explained

It can be convenient for us to simplify fractions with an exponents calculator as the tool is extremely collaborative and interactive for students.

## FAQs:

### How do you add fractional exponents having the same base?

We add them by combining the bases of the exponents and they apply the addition process of the exponents.

X5 * X3= X5+3=X8

### How do you add fractions exponents with the same denominators?

When fractional exponents have the same denominator, we need to take the denominator and add all the numerator values.

Like ⅖+⅗+⅘=9/5

### What is the quotient rule for the exponent of the same base?

The quotient rule states that we can use the one base for fractional exponents having the same base but different exponential fractions.

Like:

X4/3*X1/3=X(4+⅓)= X5/3

We can use the different quotient calculators for solving the quotients.

## Conclusion:

We commonly use the fractional exponent in the field of mathematics but need to enter only real numbers in the fractions. The fraction exponent calculator is a straightforward and simple way to solve difficult fractional exponents. The fractional exponent can be difficult to solve when we are dealing with the higher power of the Base.

## References:

From the source studypug.com: Quotient rule of exponents, Lessons, Basic Concepts

From the sourceTutorme.com: The Basics of Exponents, Fractions With Exponents, Solving Fractions With Exponents

From the source, mathsisfun.com: Whole Number Exponents ,Fractional Exponents, Try Another Fraction