# Math Worksheets Land

Math Worksheets For All Ages

# Math Worksheets Land

Math Worksheets For All Ages

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# Rational Exponent Worksheets

### Aligned Standard: 6.EE.A.1

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

### Homework Sheets

Each of these sheets gets progressively more difficult.

• Homework 1 - You will work with fractional exponents and strive to make sense of them in a simple form.
• Homework 2 - You will advance to the next level and work exponent of fractional bases. It is not as difficult as it first appears.
• Homework 3 - We now add an operation that you must evaluate as well.
• Homework 4 - This can be complicated if do not plan out the steps that you will take along the way.
• Homework 5 - You will need to draw up the steps of your approach for this one too.

### Practice Worksheets

This selection of sheets will help students better understand the sequence they should use to solve these problems.

• Practice 1 - Write each expression as a radical in simplest form.
• Practice 2 - You may leave improper fractions in the exponent.
• Practice 3 - The focus here is end off with positive exponents.
• Practice 4 - Do not forget that an operation is found within every expression.

### Quiz Sheets

It is time to see how well you can manipulate this skill.

• Quiz 1 - You will rewrite these expressions in a simple form.
• Quiz 2 - We see how you handle negative rational exponents.
• Quiz 3 - The example is really good to help elevate your mindset for all the problems on the page.
• Quiz 4 - You may find that students try to solve for the unknown variables.

### How to Simplify Expressions with Rational Expressions

When we are working with calculations that involve rational exponents, we just need to remember our basic math operations with them. It all begins by understanding the vocabulary for these types of expressions. The best way to explain this is just to jump in and take a look at an expression. Say for instance we were evaluating the expression: 3x ½. In this instance 3 serves as the coefficient. The variable (x) is the base, and the rational exponent is the fraction (½). Now that we understand all the mechanics of these expressions and what we call their parts, lets evaluate how they work with operations. When we fully understand how these operations work, we can learn to quickly simplify these expressions with ease. There are two common operations that we will work with that involve either multiplication or division.

Product of Powers - When you are multiplying two exponential values that share a common base or coefficient the product simply just requires that you find sum of the exponents. It follows the form:

ab x ac = a(b + c)

This applies whether the values of the exponents or fraction. They just need to be rational numbers. We can use this in the example: 4 ½ x 4 ¼

We can rewrite this as: 4 ½ + ¼ or 4¾.

Quotient of Powers - As is often true of division, it serves as the counterpart or polar opposite of multiplication. When we are determining the product, we added the exponents. When we are determining the quotient, we do the polar opposite, we subtract the exponents. This can be illustrated by the backbone:

ab ÷ ac = a(b - c)

Using the same example, but flipping the operation we can run this through for you: 4 ½ ÷ 4 ¼

We can rewrite this as: 4 ½ - ¼ or 4¼.

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