Fractions with Exponents Calculator

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Answer =

 

Fractions with Exponents Calculator is a free online tool that displays the simplification of the given exponent. BYJU’S online fractions with exponents calculator tool perform the calculation faster and it displays the simplified value in a fraction of seconds.

How to Use the Fractions with Exponents Calculator? 

The procedure to use the fractions with exponents calculator is as follows:

Step 1: Enter the base and the exponent value in the input field

Step 2: Now click the button “Calculate”  to get the simplified form

Step 3: Finally, the simplification of fractions with exponents will be displayed in the output field

What is Meant by Fractional Exponents?

In maths, the fractional exponents is an alternate way of expressing the roots as well as powers in the expression. The different ways to represent the fractional exponents are fractional exponents with a numerator equal to the value 1, numerator value which should be other than 1, negative fractional exponents and so on. 

Also. check: Laws of Exponents

The simplest representation of fractional exponent is x(n/k). For example, 91/2.

  • If the numerator of the exponent is equal to 1, then the representation is x1/k. It is written in the form \(\sqrt[k]{x}\)
  • If the numerator of the exponent is other than 1, then the representation is xn/k. It is represented as \(\sqrt[k]{x^{n}}\), which can also be written as \((\sqrt[k]{x})^{n}\)
  • We know that if the exponent value is positive, it tells us how many times we have to multiply the base number, whereas if the exponent value is negative, it tells us how many times we have to divide the base number.

Solved Example on Fractions with Exponents

Example 1:

Simplify the fractional exponent 641/2

Solution:

Given that, the fractional exponent is 641/2

Here, the numerator of the fractional exponent is 1, hence 641/2 is written as \(\sqrt[2]{64}\)

Therefore, 641/2 = \(\sqrt[2]{8^{2}}\)

Now, simplify the above expression, we get

641/2 = 8

Therefore, the simplification of the fractional exponent 641/2  is 8.

Example 2: 

Simplify the fractional exponent 274/3

Solution:

Given that, the fractional exponent is 274/3

Here, the numerator value of the fractional exponent is 4.

Hence, 274/3 = \((\sqrt[3]{27})^{4}\)

274/3 = 34

274/3= 81

Hence, the simplified form of the fractional exponent 274/3 is 81.

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