Dividing exponents worksheet

Dividing powers of the same base subtracts the exponents, top minus bottom. When the bottom is the bigger power the answer would carry a negative exponent, so it is written as a fraction instead.

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

Sigma Prep · sigmaprep.io/worksheets

Name

Dividing Exponents

Date Period

Simplify. Your answer should contain only positive exponents.

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



Sigma Prep · sigmaprep.io/worksheets Name Dividing ExponentsAnswer keyVersion 1 Date Period Simplify. Your answer should contain only positive exponents. $\frac{4 a x^{5}}{9 a^{3} x^{- 5}}$ $\frac{4 x^{10}}{9 a^{2}}$ $\frac{4 p^{- 3} x^{3}}{7 p x^{2}}$ $\frac{4 x}{7 p^{4}}$ $\frac{3 b x^{3}}{2 b x^{3}}$ $\frac{3}{2}$ $\frac{7 a^{3} x}{9 a^{4} x^{4}}$ $\frac{7}{9 a x^{3}}$ $\frac{6 b^{4} x^{2}}{2 b^{- 1} x^{3}}$ $\frac{3 b^{5}}{x}$ $\frac{7 b x^{5}}{4 b^{4} x^{2}}$ $\frac{7 x^{3}}{4 b^{3}}$ $\frac{8 m^{4} x^{5}}{9 m^{5} x^{4}}$ $\frac{8 x}{9 m}$ $\frac{4 n^{- 4} x}{3 n^{5} x^{5}}$ $\frac{4}{3 n^{9} x^{4}}$ $\frac{3 b^{5} x^{5}}{7 b^{- 5} x}$ $\frac{3 b^{10} x^{4}}{7}$ $\frac{2 k x^{5}}{k^{2} x^{4}}$ $\frac{2 x}{k}$ $\frac{6 n^{3} x^{2}}{7 n^{3} x^{- 5}}$ $\frac{6 x^{7}}{7}$ $\frac{3 m x^{4}}{9 m^{- 1} x^{2}}$ $\frac{m^{2} x^{2}}{3}$ $\frac{6 m^{4} x^{5}}{2 m x^{3}}$ $3 m^{3} x^{2}$ $\frac{8 x^{- 1} y}{3 x^{4} y}$ $\frac{8}{3 x^{5}}$ $\frac{5 x^{5} y}{4 x^{- 5} y^{5}}$ $\frac{5 x^{10}}{4 y^{4}}$ $\frac{r x^{5}}{2 r^{2} x^{4}}$ $\frac{x}{2 r}$ $\frac{a^{4} x^{4}}{8 a^{4} x^{- 5}}$ $\frac{x^{9}}{8}$ $\frac{4 v^{3} x}{v^{2} x}$ $4 v$ $\frac{v^{3} x^{5}}{4 v^{4} x^{3}}$ $\frac{x^{2}}{4 v}$ $\frac{8 r^{2} x^{- 4}}{9 r^{5} x}$ $\frac{8}{9 r^{3} x^{5}}$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Dividing ExponentsAnswer keyVersion 1

Date Period

Simplify. Your answer should contain only positive exponents.

$\frac{4 a x^{5}}{9 a^{3} x^{- 5}}$ $\frac{4 x^{10}}{9 a^{2}}$
$\frac{4 p^{- 3} x^{3}}{7 p x^{2}}$ $\frac{4 x}{7 p^{4}}$
$\frac{3 b x^{3}}{2 b x^{3}}$ $\frac{3}{2}$
$\frac{7 a^{3} x}{9 a^{4} x^{4}}$ $\frac{7}{9 a x^{3}}$
$\frac{6 b^{4} x^{2}}{2 b^{- 1} x^{3}}$ $\frac{3 b^{5}}{x}$
$\frac{7 b x^{5}}{4 b^{4} x^{2}}$ $\frac{7 x^{3}}{4 b^{3}}$
$\frac{8 m^{4} x^{5}}{9 m^{5} x^{4}}$ $\frac{8 x}{9 m}$
$\frac{4 n^{- 4} x}{3 n^{5} x^{5}}$ $\frac{4}{3 n^{9} x^{4}}$
$\frac{3 b^{5} x^{5}}{7 b^{- 5} x}$ $\frac{3 b^{10} x^{4}}{7}$
$\frac{2 k x^{5}}{k^{2} x^{4}}$ $\frac{2 x}{k}$
$\frac{6 n^{3} x^{2}}{7 n^{3} x^{- 5}}$ $\frac{6 x^{7}}{7}$
$\frac{3 m x^{4}}{9 m^{- 1} x^{2}}$ $\frac{m^{2} x^{2}}{3}$
$\frac{6 m^{4} x^{5}}{2 m x^{3}}$ $3 m^{3} x^{2}$
$\frac{8 x^{- 1} y}{3 x^{4} y}$ $\frac{8}{3 x^{5}}$
$\frac{5 x^{5} y}{4 x^{- 5} y^{5}}$ $\frac{5 x^{10}}{4 y^{4}}$
$\frac{r x^{5}}{2 r^{2} x^{4}}$ $\frac{x}{2 r}$
$\frac{a^{4} x^{4}}{8 a^{4} x^{- 5}}$ $\frac{x^{9}}{8}$
$\frac{4 v^{3} x}{v^{2} x}$ $4 v$
$\frac{v^{3} x^{5}}{4 v^{4} x^{3}}$ $\frac{x^{2}}{4 v}$
$\frac{8 r^{2} x^{- 4}}{9 r^{5} x}$ $\frac{8}{9 r^{3} x^{5}}$

How to do these

$\frac{r^{2}}{2 r^{3}}$

The powers subtract: 2 minus 3 is -1.
A negative power means it belongs on the bottom.

The answer is $\frac{1}{2 r}$ .

Where students go wrong

Dividing the exponents. They subtract. And a leftover negative power is not an error to be dropped: it moves the term to the other side of the fraction bar.

Also called quotient rule exponents, quotient of powers or subtracting exponents.

Questions about these worksheets

Yes. Every dividing 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 dividing 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.

Dividing the exponents. They subtract. And a leftover negative power is not an error to be dropped: it moves the term to the other side of the fraction bar.

Dividing exponents worksheet

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How to do these

Where students go wrong

Questions about these worksheets

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