Algebra 1 rational exponents worksheet

A fractional power is a root: the bottom of the fraction is which root, the top is the power. Once that clicks, every exponent rule you already know applies to radicals too.

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Pick more than one for a sheet that mixes them.



Sigma Prep · sigmaprep.io/worksheets Name Rational Exponents Date Period Rewrite or evaluate each expression. $a^{\frac{11}{6}}$ $34 3^{- \frac{4}{3}}$ $\sqrt[6]{r^{11}}$ $1 6^{- \frac{3}{2}}$ $\sqrt[6]{b^{11}}$ $102 4^{- \frac{2}{5}}$ $n^{\frac{11}{6}}$ $21 6^{- \frac{2}{3}}$ $\sqrt[7]{a^{11}}$ $21 6^{- \frac{4}{3}}$ $\sqrt[6]{y^{11}}$ $2 7^{- \frac{2}{3}}$ $\sqrt[7]{n^{10}}$ $9^{- \frac{5}{2}}$ $k^{\frac{11}{6}}$ $6 4^{- \frac{4}{3}}$ $y^{\frac{10}{7}}$ $1680 7^{- \frac{1}{5}}$ $x^{\frac{9}{7}}$ $312 5^{- \frac{4}{5}}$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Rational Exponents

Date Period

Rewrite or evaluate each expression.

$a^{\frac{11}{6}}$
$34 3^{- \frac{4}{3}}$
$\sqrt[6]{r^{11}}$
$1 6^{- \frac{3}{2}}$
$\sqrt[6]{b^{11}}$
$102 4^{- \frac{2}{5}}$
$n^{\frac{11}{6}}$
$21 6^{- \frac{2}{3}}$
$\sqrt[7]{a^{11}}$
$21 6^{- \frac{4}{3}}$
$\sqrt[6]{y^{11}}$
$2 7^{- \frac{2}{3}}$
$\sqrt[7]{n^{10}}$
$9^{- \frac{5}{2}}$
$k^{\frac{11}{6}}$
$6 4^{- \frac{4}{3}}$
$y^{\frac{10}{7}}$
$1680 7^{- \frac{1}{5}}$
$x^{\frac{9}{7}}$
$312 5^{- \frac{4}{5}}$



Sigma Prep · sigmaprep.io/worksheets Name Rational ExponentsAnswer keyVersion 1 Date Period Rewrite or evaluate each expression. $a^{\frac{11}{6}}$ $\sqrt[6]{a^{11}}$ $34 3^{- \frac{4}{3}}$ $\frac{1}{2401}$ $\sqrt[6]{r^{11}}$ $r^{\frac{11}{6}}$ $1 6^{- \frac{3}{2}}$ $\frac{1}{64}$ $\sqrt[6]{b^{11}}$ $b^{\frac{11}{6}}$ $102 4^{- \frac{2}{5}}$ $\frac{1}{16}$ $n^{\frac{11}{6}}$ $\sqrt[6]{n^{11}}$ $21 6^{- \frac{2}{3}}$ $\frac{1}{36}$ $\sqrt[7]{a^{11}}$ $a^{\frac{11}{7}}$ $21 6^{- \frac{4}{3}}$ $\frac{1}{1296}$ $\sqrt[6]{y^{11}}$ $y^{\frac{11}{6}}$ $2 7^{- \frac{2}{3}}$ $\frac{1}{9}$ $\sqrt[7]{n^{10}}$ $n^{\frac{10}{7}}$ $9^{- \frac{5}{2}}$ $\frac{1}{243}$ $k^{\frac{11}{6}}$ $\sqrt[6]{k^{11}}$ $6 4^{- \frac{4}{3}}$ $\frac{1}{256}$ $y^{\frac{10}{7}}$ $\sqrt[7]{y^{10}}$ $1680 7^{- \frac{1}{5}}$ $\frac{1}{7}$ $x^{\frac{9}{7}}$ $\sqrt[7]{x^{9}}$ $312 5^{- \frac{4}{5}}$ $\frac{1}{625}$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Rational ExponentsAnswer keyVersion 1

Date Period

Rewrite or evaluate each expression.

$a^{\frac{11}{6}}$ $\sqrt[6]{a^{11}}$
$34 3^{- \frac{4}{3}}$ $\frac{1}{2401}$
$\sqrt[6]{r^{11}}$ $r^{\frac{11}{6}}$
$1 6^{- \frac{3}{2}}$ $\frac{1}{64}$
$\sqrt[6]{b^{11}}$ $b^{\frac{11}{6}}$
$102 4^{- \frac{2}{5}}$ $\frac{1}{16}$
$n^{\frac{11}{6}}$ $\sqrt[6]{n^{11}}$
$21 6^{- \frac{2}{3}}$ $\frac{1}{36}$
$\sqrt[7]{a^{11}}$ $a^{\frac{11}{7}}$
$21 6^{- \frac{4}{3}}$ $\frac{1}{1296}$
$\sqrt[6]{y^{11}}$ $y^{\frac{11}{6}}$
$2 7^{- \frac{2}{3}}$ $\frac{1}{9}$
$\sqrt[7]{n^{10}}$ $n^{\frac{10}{7}}$
$9^{- \frac{5}{2}}$ $\frac{1}{243}$
$k^{\frac{11}{6}}$ $\sqrt[6]{k^{11}}$
$6 4^{- \frac{4}{3}}$ $\frac{1}{256}$
$y^{\frac{10}{7}}$ $\sqrt[7]{y^{10}}$
$1680 7^{- \frac{1}{5}}$ $\frac{1}{7}$
$x^{\frac{9}{7}}$ $\sqrt[7]{x^{9}}$
$312 5^{- \frac{4}{5}}$ $\frac{1}{625}$

How to do these

$8^{\frac{2}{3}}$

The bottom is 3, so take the cube root of 8.
That is 2.
The top is 2, so square it.

The answer is $4$ .

Where students go wrong

Doing the power first on a big number. 8^(2/3) is 4, and getting there via 64 is harder than it needs to be. Root first, then power, every time.

Also called fractional exponents, fractional indices or roots as powers.

What you can put on this worksheet

Swap between a root and a fractional power: $\sqrt[3]{v^{4}}$ → $v^{\frac{4}{3}}$
Work out the value: $6 4^{\frac{4}{3}}$ → $256$

Questions about these worksheets

Yes. Every rational 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 rational 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: swap between a root and a fractional power and work out the value. Tick as many as you want and set how many of each, or let it spread them evenly.

Doing the power first on a big number. 8^(2/3) is 4, and getting there via 64 is harder than it needs to be. Root first, then power, every time.

Algebra 1 rational exponents worksheet

Select your difficulty

Rational Exponents

Rational ExponentsAnswer keyVersion 1

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these rational exponents worksheets free?+

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