Negative and zero exponents worksheet

Two rules. Anything except zero raised to the zero is 1. A negative exponent means the reciprocal: 2 to the -3 is 1 over 2 cubed, and x to the -2 is 1 over x squared. Move the factor across the fraction bar and the sign of the exponent flips.

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Pick more than one for a sheet that mixes them.



Sigma Prep · sigmaprep.io/worksheets Name Zero and Negative Exponents Date Period Simplify. Write every answer with positive exponents only. $6 x^{0}$ $5 x^{2} y^{- 4}$ ${(\frac{1}{4})}^{- 1}$ ${(3 n)}^{- 3}$ $2^{- 2}$ ${(2 v^{2})}^{- 3}$ $(7 n)^{0}$ ${(5 r)}^{- 2}$ ${(\frac{1}{3})}^{- 1}$ ${(5 a^{2})}^{- 3}$ $(- 4)^{- 3}$ $9 x y^{- 1}$ $2^{- 4} \cdot 2^{3}$ ${(4 y)}^{- 3}$ $2^{- 2} \cdot 2^{1}$ $6 p^{- 1} y^{4}$ $2^{- 1} \cdot 2^{2}$ ${(4 k)}^{- 3}$ $5^{- 3}$ ${(5 b^{3})}^{- 3}$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Zero and Negative Exponents

Date Period

Simplify. Write every answer with positive exponents only.

$6 x^{0}$
$5 x^{2} y^{- 4}$
${(\frac{1}{4})}^{- 1}$
${(3 n)}^{- 3}$
$2^{- 2}$
${(2 v^{2})}^{- 3}$
$(7 n)^{0}$
${(5 r)}^{- 2}$
${(\frac{1}{3})}^{- 1}$
${(5 a^{2})}^{- 3}$
$(- 4)^{- 3}$
$9 x y^{- 1}$
$2^{- 4} \cdot 2^{3}$
${(4 y)}^{- 3}$
$2^{- 2} \cdot 2^{1}$
$6 p^{- 1} y^{4}$
$2^{- 1} \cdot 2^{2}$
${(4 k)}^{- 3}$
$5^{- 3}$
${(5 b^{3})}^{- 3}$



Sigma Prep · sigmaprep.io/worksheets Name Zero and Negative ExponentsAnswer keyVersion 1 Date Period Simplify. Write every answer with positive exponents only. $6 x^{0}$ $6$ $5 x^{2} y^{- 4}$ $\frac{5 x^{2}}{y^{4}}$ ${(\frac{1}{4})}^{- 1}$ $4$ ${(3 n)}^{- 3}$ $\frac{1}{27 n^{3}}$ $2^{- 2}$ $\frac{1}{4}$ ${(2 v^{2})}^{- 3}$ $\frac{1}{8 v^{6}}$ $(7 n)^{0}$ $1$ ${(5 r)}^{- 2}$ $\frac{1}{25 r^{2}}$ ${(\frac{1}{3})}^{- 1}$ $3$ ${(5 a^{2})}^{- 3}$ $\frac{1}{125 a^{6}}$ $(- 4)^{- 3}$ $- \frac{1}{64}$ $9 x y^{- 1}$ $\frac{9 x}{y}$ $2^{- 4} \cdot 2^{3}$ $\frac{1}{2}$ ${(4 y)}^{- 3}$ $\frac{1}{64 y^{3}}$ $2^{- 2} \cdot 2^{1}$ $\frac{1}{2}$ $6 p^{- 1} y^{4}$ $\frac{6 y^{4}}{p}$ $2^{- 1} \cdot 2^{2}$ $2$ ${(4 k)}^{- 3}$ $\frac{1}{64 k^{3}}$ $5^{- 3}$ $\frac{1}{125}$ ${(5 b^{3})}^{- 3}$ $\frac{1}{125 b^{9}}$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Zero and Negative ExponentsAnswer keyVersion 1

Date Period

Simplify. Write every answer with positive exponents only.

$6 x^{0}$ $6$
$5 x^{2} y^{- 4}$ $\frac{5 x^{2}}{y^{4}}$
${(\frac{1}{4})}^{- 1}$ $4$
${(3 n)}^{- 3}$ $\frac{1}{27 n^{3}}$
$2^{- 2}$ $\frac{1}{4}$
${(2 v^{2})}^{- 3}$ $\frac{1}{8 v^{6}}$
$(7 n)^{0}$ $1$
${(5 r)}^{- 2}$ $\frac{1}{25 r^{2}}$
${(\frac{1}{3})}^{- 1}$ $3$
${(5 a^{2})}^{- 3}$ $\frac{1}{125 a^{6}}$
$(- 4)^{- 3}$ $- \frac{1}{64}$
$9 x y^{- 1}$ $\frac{9 x}{y}$
$2^{- 4} \cdot 2^{3}$ $\frac{1}{2}$
${(4 y)}^{- 3}$ $\frac{1}{64 y^{3}}$
$2^{- 2} \cdot 2^{1}$ $\frac{1}{2}$
$6 p^{- 1} y^{4}$ $\frac{6 y^{4}}{p}$
$2^{- 1} \cdot 2^{2}$ $2$
${(4 k)}^{- 3}$ $\frac{1}{64 k^{3}}$
$5^{- 3}$ $\frac{1}{125}$
${(5 b^{3})}^{- 3}$ $\frac{1}{125 b^{9}}$

How to do these

$4 x^{- 2} y^{3}$

The 4 and the y stay where they are; their exponents are not negative.
x to the -2 moves down and becomes x squared.

The answer is $\frac{4 y^{3}}{x^{2}}$ .

Where students go wrong

Making the answer negative. 2 to the -3 is one eighth, not negative eight. The minus sign on the exponent is about flipping, not about sign.

Also called negative exponents, zero exponent rule, positive exponents only or rewriting negative exponents.

What you can put on this worksheet

Evaluate a zero or negative exponent: $5^{- 3}$ → $\frac{1}{125}$
Rewrite with positive exponents: $v^{- 4}$ → $\frac{1}{v^{4}}$

Questions about these worksheets

Yes. Every negative and zero exponents sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Algebra 1 is usually taken around 8th or 9th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the negative and zero exponents questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 2: evaluate a zero or negative exponent and rewrite with positive exponents. Tick as many as you want and set how many of each, or let it spread them evenly.

Making the answer negative. 2 to the -3 is one eighth, not negative eight. The minus sign on the exponent is about flipping, not about sign.

Negative and zero exponents worksheet

Select your difficulty

Zero and Negative Exponents

Zero and Negative ExponentsAnswer keyVersion 1

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

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