Properties of exponents worksheet

The three rules, mixed or one at a time. Easy keeps everything positive and to one letter; the harder levels bring in negative exponents and up to three letters, which is where students start losing track.

Select your difficulty

Pick more than one for a sheet that mixes them.



Sigma Prep · sigmaprep.io/worksheets Name Properties of Exponents Date Period Simplify. Your answer should contain only positive exponents. $9 a^{4} \cdot \frac{7}{a^{3}}$ ${(2 p^{3} x^{3})}^{- 1}$ $\frac{3 b x}{2 b^{3} x^{2}}$ $3 x^{4} \cdot \frac{5}{x^{3}}$ ${(5 r^{4})}^{3}$ $\frac{3 x y^{2}}{2 x^{2} y^{4}}$ $\frac{8}{r^{2} x^{3}} \cdot \frac{3 x^{2}}{r^{4}}$ ${(9 a^{5} x^{4})}^{3}$ $\frac{5 x^{5} y}{9 x^{2} y}$ $2 r^{4} \cdot 4 r$ ${(6 n^{2})}^{0}$ $\frac{3 v x^{5}}{2 v^{- 5} x^{2}}$ $\frac{3}{a x} \cdot \frac{5 a^{3}}{x^{3}}$ ${(9 b^{2} x^{5})}^{4}$ $\frac{8 x y^{5}}{x y^{2}}$ $\frac{2 b^{4}}{x} \cdot \frac{3}{b^{3} x^{4}}$ ${(3 x^{4} y^{4})}^{- 1}$ $\frac{m^{- 2} x^{5}}{8 m^{2} x^{5}}$ $\frac{3}{m^{4}} \cdot 4 m^{3}$ ${(5 a^{2})}^{3}$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Properties of Exponents

Date Period

Simplify. Your answer should contain only positive exponents.

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



Sigma Prep · sigmaprep.io/worksheets Name Properties of ExponentsAnswer keyVersion 1 Date Period Simplify. Your answer should contain only positive exponents. $9 a^{4} \cdot \frac{7}{a^{3}}$ $63 a$ ${(2 p^{3} x^{3})}^{- 1}$ $\frac{1}{2 p^{3} x^{3}}$ $\frac{3 b x}{2 b^{3} x^{2}}$ $\frac{3}{2 b^{2} x}$ $3 x^{4} \cdot \frac{5}{x^{3}}$ $15 x$ ${(5 r^{4})}^{3}$ $125 r^{12}$ $\frac{3 x y^{2}}{2 x^{2} y^{4}}$ $\frac{3}{2 x y^{2}}$ $\frac{8}{r^{2} x^{3}} \cdot \frac{3 x^{2}}{r^{4}}$ $\frac{24}{r^{6} x}$ ${(9 a^{5} x^{4})}^{3}$ $729 a^{15} x^{12}$ $\frac{5 x^{5} y}{9 x^{2} y}$ $\frac{5 x^{3}}{9}$ $2 r^{4} \cdot 4 r$ $8 r^{5}$ ${(6 n^{2})}^{0}$ $1$ $\frac{3 v x^{5}}{2 v^{- 5} x^{2}}$ $\frac{3 v^{6} x^{3}}{2}$ $\frac{3}{a x} \cdot \frac{5 a^{3}}{x^{3}}$ $\frac{15 a^{2}}{x^{4}}$ ${(9 b^{2} x^{5})}^{4}$ $6561 b^{8} x^{20}$ $\frac{8 x y^{5}}{x y^{2}}$ $8 y^{3}$ $\frac{2 b^{4}}{x} \cdot \frac{3}{b^{3} x^{4}}$ $\frac{6 b}{x^{5}}$ ${(3 x^{4} y^{4})}^{- 1}$ $\frac{1}{3 x^{4} y^{4}}$ $\frac{m^{- 2} x^{5}}{8 m^{2} x^{5}}$ $\frac{1}{8 m^{4}}$ $\frac{3}{m^{4}} \cdot 4 m^{3}$ $\frac{12}{m}$ ${(5 a^{2})}^{3}$ $125 a^{6}$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Properties of ExponentsAnswer keyVersion 1

Date Period

Simplify. Your answer should contain only positive exponents.

$9 a^{4} \cdot \frac{7}{a^{3}}$ $63 a$
${(2 p^{3} x^{3})}^{- 1}$ $\frac{1}{2 p^{3} x^{3}}$
$\frac{3 b x}{2 b^{3} x^{2}}$ $\frac{3}{2 b^{2} x}$
$3 x^{4} \cdot \frac{5}{x^{3}}$ $15 x$
${(5 r^{4})}^{3}$ $125 r^{12}$
$\frac{3 x y^{2}}{2 x^{2} y^{4}}$ $\frac{3}{2 x y^{2}}$
$\frac{8}{r^{2} x^{3}} \cdot \frac{3 x^{2}}{r^{4}}$ $\frac{24}{r^{6} x}$
${(9 a^{5} x^{4})}^{3}$ $729 a^{15} x^{12}$
$\frac{5 x^{5} y}{9 x^{2} y}$ $\frac{5 x^{3}}{9}$
$2 r^{4} \cdot 4 r$ $8 r^{5}$
${(6 n^{2})}^{0}$ $1$
$\frac{3 v x^{5}}{2 v^{- 5} x^{2}}$ $\frac{3 v^{6} x^{3}}{2}$
$\frac{3}{a x} \cdot \frac{5 a^{3}}{x^{3}}$ $\frac{15 a^{2}}{x^{4}}$
${(9 b^{2} x^{5})}^{4}$ $6561 b^{8} x^{20}$
$\frac{8 x y^{5}}{x y^{2}}$ $8 y^{3}$
$\frac{2 b^{4}}{x} \cdot \frac{3}{b^{3} x^{4}}$ $\frac{6 b}{x^{5}}$
${(3 x^{4} y^{4})}^{- 1}$ $\frac{1}{3 x^{4} y^{4}}$
$\frac{m^{- 2} x^{5}}{8 m^{2} x^{5}}$ $\frac{1}{8 m^{4}}$
$\frac{3}{m^{4}} \cdot 4 m^{3}$ $\frac{12}{m}$
${(5 a^{2})}^{3}$ $125 a^{6}$

How to do these

$2 m^{2} \cdot 2 m^{3}$

Multiply the numbers: 2 times 2 is 4.
Multiplying powers of the same letter adds the exponents.
2 + 3 = 5.

The answer is $4 m^{5}$ .

Where students go wrong

Multiplying the exponents instead of adding them. m² · m³ is m⁵, not m⁶, and the rule only flips to multiplying when a power is raised to a power. The other one is leaving a negative exponent in the answer: 2x⁻¹ is not finished, it is 2 over x.

Also called exponent rules, the laws of exponents, laws of indices or power rules.

What you can put on this worksheet

Multiplying: $4 v^{3} \cdot 3 v$ → $12 v^{4}$
A power of a power: ${(4 v^{3})}^{2}$ → $16 v^{6}$
Dividing: $\frac{2 v^{4}}{2 v^{5}}$ → $\frac{1}{v}$

Questions about these worksheets

Yes. Every properties of 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 properties of 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 3: multiplying, a power of a power and dividing. Tick as many as you want and set how many of each, or let it spread them evenly.

Properties of exponents worksheet

Select your difficulty

Properties of Exponents

Properties of ExponentsAnswer keyVersion 1

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these properties of exponents worksheets free?+

Do the properties of exponents worksheets come with an answer key?+

Are these properties of exponents worksheets printable?+

What grade are these properties of exponents worksheets for?+

Can I get a different version of the same properties of exponents worksheet?+

Is this a free alternative to Kuta Software for properties of exponents?+

Can I choose how hard the properties of exponents questions are?+

What kinds of question are on a properties of exponents worksheet?+

What do students get wrong with properties of exponents?+