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Grade 6 Math Worksheets

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.

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 2^{3}, which is 1/2^{3}.
Therefore, 2^{-3} = 1/(2^{3}) = 1/8 = 0.125.

(1/3)^{-4}:

This means taking the reciprocal of (1/3)^{4}, which is 3^{4}.
Therefore, (1/3)^{-4} = 3^{4} = 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 0.2^{2}, which is 1/0.2^{2}.
Therefore, 0.2^{-2} = 1/(0.2^{2}) = 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.

Click on the following worksheet to get a printable pdf document.

Scroll down the page for 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

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