Fraction Exponent Calculator

Are you finding it difficult to solve fraction with exponent? If yes, then this fraction exponent calculator will help you calculate the results quickly and accurately. The tool considers the exponents as fractions and solves for the dth root of a number x that is raised to a power n. With that, you get step-wise calculations and all possible roots (Real & Imaginary) of the expression entered.

Instructions to Use Our Fraction Exponent Calculator:

• Add the values of base, numerator, and denominator
• Tap 'Calculate'

What Is a Fraction Exponent? 

Fraction exponents are a way of writing powers of numbers as fractions.

While writing rational exponents (another possible name for fractional powers), you must know that:

• The numerator is the power of the term that is written inside the root
• The denominator is the power of the root itself

General Form:

The standard form of rational exponent is as follows:

$$ x^{\dfrac{n}{d}} $$

where;

• x = Base of the expression given
• n = Numerator of the exponential expression
• d = Denominator of the exponential expression

General Fraction Exponents:

Exponent	Name of the exponent	Indication
1/2	Square root	a1/2 = √a
1/3	Cube root	a1/3 = 3√a
1/4	Fourth root	a1/4 = 4√a

Fractional Exponents Rules:

$$ a^{\dfrac{1}{m}} \times a^{\dfrac{1}{n}} = a^{\dfrac{1}{m}+\dfrac{1}{n}} $$

$$ \dfrac{a^{\dfrac{1}{m}}}{a^{\dfrac{1}{n}}} = a^{\dfrac{1}{m}-\dfrac{1}{n}} $$

$$ a^{1/m} \times b^{1/m} = (ab)^{1/m} $$

$$ a^{1/m} \div b^{1/m} = (a \div b)^{1/m} $$

$$ a^{-m/n} = (1/a)^{m/n} $$

How to Solve Fractions with Exponents?

To solve fractional exponent problems, you need to understand how power and root combinations work. Let’s learn this together!

• Recognize the Expression: Analyze if the given expression is a fractional exponent or not. For instance, you may see if it is in the form mentioned above.
• Convert to Radicals Notation: The next step is to convert the given fractional exponent to an equivalent radical expression. e.g; if you have \(x^{n}{d}\), it will be written as \(\sqrt[d]{n}\)
• Solve for Simplification: This is the last step! Here you need to evaluate the radical expression and then solve for any arithmetic operation to reduce the expression to simplest form.

The above steps might help you determine results, but the procedure can be time-consuming. This is why using our fraction exponent calculator helps you get efficient results in moments that save you time while making no compromise with accuracy.

Example:

How to simplify fractional exponent given below?

$$ 3^{\dfrac{2}{7}} $$

Solution:

Step # 01:

As 3 is the base and the exponent is 2/7, so we have:

This indicates that we have to determine the seventh root of 3 that will be raised to the power of 2, such that:

\(3^{2}{7} = \left(3^{\dfrac{1}{7}}\right)\), raised to the power of 2, such that:

$$ \root7\of3^2 $$

Step # 02:

The principal (original) root of the given expression is given as:

$$ \root7\of3 $$

Simplifying to get the answer:

$$ = 1.3687381066422 $$

Negative Fractional Exponents:

Negative fraction exponents are the expressions that contain the inverted number x raised to the positive fractional power. 

The fraction exponent calculator also shows complete work for negative rational exponents. Whatever the expression you enter in it, the tool will provide you with step-by-step calculations to understand the solution better.

Example:

Let’s solve \(3^{\dfrac{-2}{3}}\)!

Step # 01:

$$ 3^{\dfrac{-2}{3}} = \dfrac{1}{4^{\dfrac{2}{3}}} $$

Step # 02:

$$ 3^{\dfrac{-2}{3}} = \sqrt[3]{3^{-2}} $$

Step # 03:

$$ 3^{\dfrac{-2}{3}} = \sqrt[3]{0.11111111111111} $$

Step # 04:

$$ 3^{\dfrac{-2}{3}} = \sqrt[3 ]{0.11111111111111} = 0.480749857 $$