Law of Exponents Worksheets

There are six sets of law of exponents worksheets:

• Product Rule
  
• Quotient Rule
  
• Power Rule
  
• Negative Exponents
  
• Fractional exponents
  
• Laws of Exponents
  

Examples, solutions, videos, and worksheets to help Grade 7 and Grade 8 students learn how to use the law of exponents.

The laws of exponents, also known as the rules of exponents, are a set of mathematical principles that govern how exponents (also called powers) work with numbers and expressions.

How to use the laws of exponents?

There are three sets of using the laws of exponents worksheets.

• Law of Exponents (Whole Number Exponents).
• Law of Exponents (Include Negative Exponents).
• Law of Exponents (Include Fractional Exponents).

The laws of exponents, also known as the rules of exponents, are a set of mathematical principles that govern how exponents (also called powers) work with numbers and expressions. Here are the basic laws of exponents:

1. Product Rule: When you multiply two exponential expressions with the same base, you can add their exponents.
   a^m ⋅ aⁿ = a^{m + n}
   For example, 2³ ⋅ 2⁴ = 2³⁺⁴ = 2
2. Quotient Rule: When you divide two exponential expressions with the same base, you can subtract the exponent in the denominator from the exponent in the numerator.
   a^m/aⁿ = ^m-n
   For example, 5⁶/5⁴ = 5^6-4 = 5²
3. Power Rule: When you raise an exponential expression to another exponent, you can multiply the exponents.
   (a^m)ⁿ = a^{m ⋅ n}
   For example, (3²)⁴ = 3^{2 ⋅ 4} = 3⁸
4. Zero Exponent Rule: Any nonzero number raised to the power of zero is equal to 1.
   a⁰ = 1
   For example, 5⁰ = 1
5. Negative Exponent Rule: To convert a negative exponent to a positive one, take the reciprocal of the base and change the sign of the exponent.
   a^-m = 1/^m
   For example, 2^-3 = 1/2³ = 1/8

Have a look at this video if you need to review the Laws of Exponents.

• Laws of Exponents

Click on the following worksheet to get a printable pdf document.
Scroll down the page for more Law of Exponents Worksheets.

 

More Law of Exponents Worksheets

Printable
(Answers on the second page.)
Law of Exponents Worksheet #1 (Whole Number Exponents)
Law of Exponents Worksheet #2 (Include Negative Exponents)
Law of Exponents Worksheet #3 (Include Fractional Exponents)

Online
Apply Law of Exponents (multiply)
Apply Law of Exponents (mixed)

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Laws of Exponents

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