# Fractional Exponents Worksheets

A fractional exponent is just an exponent that is a fraction. These are often used to represent powers and roots in tandem. For the most part, you will be learning how to simplify values that are found in this form. As you advance, this form of notation will be found in many precalculus curriculums. At that point, you we learn how to process compound operations in this form of notation. This form of math is used primarily by the financial world to calculate things like interest, depreciation, and future inflation. While this math may seem sophisticated and confusing, once you master it, your eyes will be wide open in financial markets. These worksheets and lessons can help students become comfortable using fractions that have attached exponents.

### Aligned Standard: HSN.RN.A.1

- Step-by-Step Lesson- We work with positive and negative whole numbers on fractions.
- Guided Lesson - Breakdown the core structure of a fraction with various exponential forms.
- Guided Lesson Explanation - Each problem takes a step to the next level.
- Practice Worksheet - This worksheet is entirely positive exponents to help students gain some success.
- Positive and Negative Worksheet - Both skills are incorporated here.

- Answer Keys - These are for all the unlocked materials above.

### Positive Exponent Practice Sheets

Answer keys are found as the second page.

- Practice 2 - Solve for the following problems.
- Practice 3 - These fractions will drive you down the turnpike.
- Practice 4 - The help you need on these.
- Practice 5 - The 9th exponent will throw you at first.

### Mixed Exponent Practice

More plus and minus exponents to juggle.

- Practice 2 - How do we steer you with this one?
- Practice 3 - The negative will throw you.
- Practice 4 - What is the negative of a negative?
- Practice 5 - A solid finisher practice worksheet.

### What’s With Fractional Exponents?

Exponents are one of the most basic components of any beginner level math class. They offer another way of notating a mathematical value. Exponents define the value of a number and are often used for problem solving and simplifying purposes. They can affect fractions the same way as they impact a whole number. Exponents can also help represent fractions into whole numbers and vice versa.

Exponents themselves can be represented as whole numbers and fractions. Let's try understanding them with the help of examples. First, we look at the whole number exponents. It is important to know that the exponents represent how many times a number will be multiplied with itself. For example, 4^{2} = 4 x 4 = 16. Another example will be 6^{3} = 6 x 6 x 6 = 215.

There are also fractional exponents or exponents written in the form of fraction. They can be restated as roots when you work with them mathematically. Let’s take some time to explore this concept.

You might be asked to evaluate the following: 7^{½}.

This can be restated as the square root of the base or √7. As that fraction lessens you can evaluate it in much the same way. So a base number with an exponent to the ⅓ would be a cube root and a base number with an exponent to the ¼ would be the 4th root. Let’s put it to work for us:

7^{⅓} = ^{3}√7.

7^{¼} = ^{4}√7.

The general rule for working with fractional exponents x^{1/n} = The n-th root of x. We can restate this to make it workable as: x^{1/n} = ^{n}√x.

When it comes to more difficult fractional exponents, we need to consider the parts of the fraction. If we consider a fraction such as (a/b), we can split this into two parts: (a) the whole number part and (1/b) the fractional portion. There are two methods for determining the end value of something in this notation. Which is best to use is entirely based on the situation that you find yourself in at the time.

x^{a/b} = ^{b}√x^{a}.

x^{a/b} = (^{b}√x)^{a}.