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How to Solve Fractions With Exponents

Fractions with exponents: graphing notebook with formulas

Exponents and fractions are complicated enough on their own. Why do we have to involve fractions with exponents? Though solving fractional exponents seems difficult, breaking down and simplifying the process makes it much easier to tackle.

The Basics of Exponents

First, let's give you a little refresher on how exponents work. Here is an example of an exponential expression:

Fractions with exponents: exponential expression example

In this example, x represents the value that is being multiplied by itself. N represents the exponent. The basic rules of exponents say the base number x will be multiplied by itself n times.

Here’s an example of one of the most common exponents: an exponent of two. Solving this is also called squaring or raising the base to the second power.

Fractions with exponents: exponent of two

Fractions With Exponents

Fractions with exponents, also known as powers of fractions, are a little bit different. When the base number is a fraction rather than a whole number, you are multiplying fractions by themselves however many times the exponent indicates:

powers of fractions

In the practice problem above, both the numerator and denominator within the parentheses are being raised to the third power.

The correct answer for a fraction with exponents will always be a fraction. The next step is multiplying out the exponents. To put the fraction in decimal form, you’ll find the quotient by dividing one cubed quantity by the other:

cubed quantity

Solving Fractions With Exponents

To solve fractions with exponents, review the rules of exponents. You’ll distribute the exponent to the full fraction if indicated. Then, you’ll multiply the full fraction, the base, by itself the number of times directed by the exponent.

Both exponents and fractions are important algebraic concepts. Learning how to solve fractions with exponents is also valuable.

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