Zero and negative exponents worksheet

Thirty-six grade 8 questions: zero exponents, negative powers as fractions, powers of 10 as decimals, writing fractions as powers and using the rules.

Download the free zero and negative exponents worksheet (PDF)

What’s on the worksheet

• 36 questions on zero and negative exponents, sized for US Letter paper
• 2 pages of questions plus an answer key on the last page
• Written for grade 8, matching Common Core 8.EE.A.1
• Name and date lines at the top, and room to show the work

Sample questions from this worksheet

1. (−7)⁰ =
2. 4⁻² =
3. 10⁻⁴ =
4. Write 1/8 as a power with a negative exponent.
5. 2⁵ × 2⁻² =
6. 10⁻² × 10⁻¹ =

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Need another page for extra practice, a retake or a second group in class? The free Mathify Kids test maker builds a fresh zero and negative exponents worksheet with different numbers every time. Choose how many questions, print it with its own answer key, or let your child take it on screen and see the score straight away.

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Zero and negative exponents: a worked example (2⁻³ and 10⁻²)

How to use it at home and in class

At home

Start with the box on page 2. The pattern of halving from 2³ down to 2⁻³ explains both the zero rule and negative exponents better than any rule to learn. In Part C, the exponent tells you which place the 1 lands in: 10⁻³ = 0.001, the thousandths place. Part E uses the product rule with negative numbers, so it is good practice with integers too. The exponent rules lesson covers the rules, and scientific notation is where negative powers of 10 are used most. Ten problems a day works better than a whole sheet at once. Mark them together with the answer key, then ask your child to explain one they got wrong: finding the mistake themselves is where the learning happens.

In class

Use the first row as a warm-up, a full page for independent practice, or five questions as an exit ticket. For a retake or a second group, make a new version with the test maker so every child gets different numbers.

Mistakes to watch for

• Making the answer negative, so 2⁻³ becomes −8 instead of 1/8.
• Multiplying the base by the exponent, so 4⁻² becomes −8 instead of 1/16.
• Writing 7⁰ = 0 or 7⁰ = 7. Any non-zero number to the power 0 is 1.
• Putting one zero too many or too few, so 10⁻⁴ is written as 0.001 instead of 0.0001.

What to practice before and after zero and negative exponents

• Before: exponent rules. If this sheet is a struggle, go back a step.
• After: scientific notation, once this one is mostly right.
• Learn it first: the zero and negative exponents lesson.