Exponent Rules Worksheets

Free Exponent Rules Worksheets and Answer Keys

Looking for free Exponent Rules Worksheets to help practice and sharpen your skills?

Below you will find a collection of pdf worksheets that you can easily download and print. Each exponent rules worksheet includes a complete answer key and reference guide at the top of the page.

You can easily download any of the free exponents rules worksheets by clicking on the blue text links. Once you click on the link, you will see the PDF preview that will allow you to either download the worksheet as a PDF file or to print the worksheet.

Below you will find links to download your free practice worksheets. If you need extra help with understanding the exponent rules, continue past the worksheet section to access a short recap of the exponent rules.

Note that all of the free exponent rules worksheets in the library below are sample activities from the Mashup Math Algebra Infinite Worksheet Library available on our website. | Quick Links: How to Download/Print

Exponent Rules Worksheets

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Exponent Rules: Quick Recap

If you are struggling with completing any of the free exponents worksheets above, then it would be a great idea to recap the exponent rules and how to apply them to solve math problems.

The exponent rules, which are often referred to as the laws of exponents, are a set of mathematical rules for simplifying expressions involving exponents.

The chart shown in Figure 02 below highlights the six most important exponent rules:

• The Zero Exponent Rule: a⁰=1

• The Product Rule: a^b x a^c = a^(b+c)

• The Quotient Rule: a^b ➗ a^c = a^(b-c)

• The Power of a Power Rule: (a^b)^c = a^(bc)

• The Power of a Product Rule: (ab)^c = a^b x a^c

• The Negative Exponent Rule: a^-b = 1/(a^b)

Now, let’s quickly review each of the six exponent rules. If you can remember and understand these laws of exponents, you will be able to solve any of the problems that are included on the worksheets above. Additionally, you will need to have a strong understanding of the exponent rules in order to be successful as you move onto higher levels of algebra.

The Zero Exponent Rule: a⁰=1

The zero exponent rule states that any expression raised to the power of 0 equals 1.

For example,

• 8⁰=1

While this exponent rule is relatively simple, it is incredible important as many students incorrectly believe that any value raised to the power of zero is equal to zero (which, of course, is not true).

The Product Rule: a^b x a^c = a^(b+c)

The product rules states that whenever you are multiplying two expressions with the same base, you can simplify it by adding the exponents together and keeping the base the same.

For example,

• 7³ x 7² = 7⁵

In short, you can simply add the two exponents together and keep the base as is.

The Quotient Rule: a^b ➗ a^c = a^(b-c)

The quotient rules states that whenever you are dividing two expressions with the same base, you can simplify it by finding the difference of the exponents and keeping the base the same.

For example,

• 10⁵ / 10² = 10³

In short, you can simply subtract the second exponent from the first exponent and keep the base as is.

The Power of a Power Rule: (a^b)^c = a^(bc)

The power of a power rules states that whenever you are raising an expression with an exponent to another exponent, it can be simplified by finding the product of the two exponents and keeping the same base.

For example,

• (x³)⁴ = x¹²

The Power of a Product Rule: (ab)^c = a^b x a^c

The power of a power rules states that whenever you are raising an entire product by an exponent, you can simplify it by distributing the exponent to each term of the product.,

For example,

• (xy)³ = x³y³

Negative Exponent Rule: a^-b = 1/(a^b)

The negative exponent rule states that whenever you have a base raised to a negative exponent, you can simplify it by rewriting it as a fraction where the same base with the positive form of the exponent is written as a fraction with a numerator of 1.

For example,

• 3^-2 = 1/(3^2)

Do you need more help with understanding the exponent rules (and how to complete the free exponent worksheets shared above)?

Check out our free step-by-step guide to the Laws of Exponents, which includes deeper explanations of each exponent rule along with several addition practice examples.

The more that you practice and learn the laws of exponents, you will be able to work with more and more complex algebraic expressions as you continue your mathematical journey from middle school math all the way to advanced algebra.