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# Power of Fractions

The power of a fraction is the result of raising a fraction to a certain exponent. An exponent is a whole number that represents the number of times the base (the fraction) is multiplied by itself.

In this article, we will cover some solved examples to understand the concept better.

Let us look at an example: This means that (1/2) raised to the 3rd power (1/2^3) is equal to 1/8.

When raising a fraction to a power, both the numerator and denominator of the fraction are raised to that power. For example: In this example, both the numerator and denominator are raised to the power of 2.

It’s important to note that when an exponent is a negative number, the fraction should be flipped and the exponent should be changed to positive. For example: And when the exponent is a fraction, the power of a fraction is represented by a root. For example: In general, when raising a fraction to a power, the numerator and denominator are both raised to that power. It’s also important to be aware of the properties of exponentiation and the rules of operations of the exponents, such as the product of exponents and the quotient of exponents.

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## More Examples Explanation: This example shows how to raise a fraction to power. In this case, (1/2) is being raised to the power of 4. To find the result, we multiply the fraction by itself 4 times. So, (1/2) * (1/2) * (1/2) * (1/2) = 1/16. ## Power of Fractions FAQS

##### Can the numerator and denominator of a fraction be raised to different powers?

No, when raising a fraction to a power, both the numerator and denominator are raised to the same power.

##### What happens when a fraction is raised to a negative power?

When a fraction is raised to a negative power, the fraction is flipped and the exponent is.

##### How to handle the power of a fraction when the exponent is a fraction?

When the exponent is a fraction, the power of a fraction is represented by a root. For example, (2/3)^(1/2) = √(2/3)

##### Can we simplify the power of a fraction?

Yes, we can simplify the power of a fraction by following the rules of exponentiation, such as the product of exponents and the quotient of exponents.

##### Can we add or subtract the power of a fraction?

It depends on the exponents and the base, you can only add or subtract the power of a fraction if the exponents and the base are the same.

##### How to handle the power of a fraction when the exponent is a decimal?

When the exponent is a decimal, you can convert it to a fraction by finding the closest fraction representation of the decimal and raising the fraction to that power. Gloria Mathew writes on math topics for K-12. A trained writer and communicator, she makes math accessible and understandable to students at all levels. Her ability to explain complex math concepts with easy to understand examples helps students master math. LinkedIn

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