Negative Exponents Worksheet

There are seven sets of exponents worksheets:

• Squares & cubes
  
• Squares & square roots
  
• Cubes & cube roots
  
• Whole number exponents
  
• Negative whole number exponents
  
• Unit fraction exponents (positive or negative)
  
• Fractional exponents (positive or negative)

Examples, solutions, videos, and worksheets to help Grade 6 students learn how to evaluate numbers with negative exponents. The number, also called the base, can be a positive or negative whole number, a positive or negative fraction, a positive or negative decimal.

How to evaluate numbers with negative exponents?

There are four sets of negative exponent worksheets:

• Positive Whole Number Base
• Negative Whole Number Base
• Fractional Base (Positive or Negative)
• Decimal Base (Positive or Negative)

When a number is raised to a negative exponent, it means that we take the reciprocal of that number raised to the positive exponent.

Here are some examples:

2^-3:
This means taking the reciprocal of 2³, which is 1/2³. Therefore, 2^-3 = 1/(2³) = 1/8 = 0.125.

(1/3)^-4:
This means taking the reciprocal of (1/3)⁴, which is 3⁴. Therefore, (1/3)^-4 = 3⁴ = 81.

(2/3)^-2:
This means taking the reciprocal of (2/3)², which is (3/2)². Therefore, (2/3)^-2 = (3/2)² = 9/4.

0.2^-2:
This means taking the reciprocal of 0.2², which is 1/0.2². Therefore, 0.2^-2 = 1/(0.2²) = 1/0.04 = 25.

We can also change the decimals to fractions before evaluating.
0.2^-2 = (2/10)^-2 = (10/2)² = 100/4 = 25

So, when dealing with negative exponents, you can think of it as taking the reciprocal of the positive exponent.

 

• Printable & Online Exponent Worksheets

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

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

Have a look at this video if you need to review how to evaluate negative exponents.

• How to Solve Negative Exponents

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

 

More Negative Exponents Worksheets

Printable
(Answers on the second page.)
Negative Exponents Worksheet #1 (Positive Whole Number Bases)
Negative Exponents Worksheet #2 (Negative Whole Number Bases)
Negative Exponents Worksheet #3 (Positive or Negative Fractional Bases)
Negative Exponents Worksheet #4 (Positive or Negative Decimal Bases)

Generated
Squares with bases 0 to 10
Squares with bases 2 to 20
Squares with bases -10 to 0
Squares with bases -20 to 0

Cubes with bases 0 to 10
Cubes with bases 2 to 20
Cubes with bases -10 to 0
Cubes with bases -20 to 0

Related Lessons & Worksheets

Exponents

More Printable Worksheets

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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