Negative Exponents Worksheet

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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.

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

Exponents
More Printable Worksheets

Free Exponent Games Online
Multiply Exponents	Divide Exponents	Power of a Power
Power of a Product	Negative Exponents	Fractional Exponents

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