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## Introduction to Fractional Exponents

Fractional Exponents – Explanation Different Functions and Solved Examples.

A fractional exponent is a number that is expressed as a fractional power. For example, the number 3/2 is a fractional exponent. This number can be written as the following:

3/2 = (3 × 2)1/2

In other words, 3/2 is equal to 3 raised to the 1/2 power.

A fractional exponent can also be represented as a radical. For example, the number 3/2 can also be written as the following:

3/2 = √(3 × 2)

This is because the square root of a number is the same as the number raised to the 1/2 power.

## Define Fractional Exponent

A fractional exponent is a number that is expressed as the power to a power. It is written as the base number raised to a fractional power. For example, the fractional exponent of 2 is 1/2, which means that the number is raised to the 1/2 power. The fractional exponent of 3 is 1/3, which means that the number is raised to the 1/3 power.

## Fractional Exponent Laws

There are three fractional exponent laws which are used to manipulate fractional exponents.

The first law states that the product of two powers with the same fractional exponent is also a power with that fractional exponent.

For example, if \(x^{1/2} \cdot y^{1/2} = z^{1/2}\), then \(x = z^{1/2}\) and \(y = z^{1/2}\).

The second law states that the quotient of two powers with the same fractional exponent is also a power with that fractional exponent.

For example, if \(x^{1/2} \div y^{1/2} = z^{1/2}\), then \(x = z^{1/2}\) and \(y = 0\).

The third law states that the power to a power with a fractional exponent is the same power with that fractional exponent.

For example, if \(x^{1/2}^3 = z^{1/2}\), then \(x = z^{1/2}\).

## How Negative Fractional Exponent Works?

A negative fractional exponent is used to define a power that is less than 1. In physics, this is known as a “decaying exponential.” In mathematical terms, a negative fractional exponent can be written as:

a-n = 1/(1+n)

For example, if we want to calculate the value of a-0.5, we would use the following equation:

1/(1+0.5) = 1/1.5 = 0.667

This means that a-0.5 is equal to 0.667, or 66.7%.

## How to Multiply Fractional Exponents With the Same Base?

In mathematics, multiplying fractional exponents with the same base is a very simple process. To do this, all you have to do is add the exponents together. For example, if you have the fractional exponent 3/2, you would simply add the exponents together to get 5/2. This is because 3/2 is equal to 1.5, and 5/2 is equal to 2.5.

There are a few things to keep in mind when multiplying fractional exponents with the same base. First, the base must be the same for both exponents. Second, you must make sure that the fractions are in the same form. Lastly, the exponents must be integers.

If you are multiplying fractional exponents with different bases, you must convert the bases to the same base before multiplying the exponents. For example, if you are multiplying the fractional exponent 3/4 and the fractional exponent 2/5, you would first convert 3/4 to 12/16 and 2/5 to 10/25. After converting the bases, you would then add the exponents together to get 22/25. Fractional Exponents – Explanation, Different Functions, and Solved Examples.

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