Power of Fractions

Grade 6 Math Worksheets

All of these are used in our day-to-day life. We use these problems to calculate certain things, like the distance of Mars from the planet Earth, calculated in light-years.

An exponent is a number that is raised to a base. But what do we mean by an Exponent?

Learn Math concepts from our 6th grade math tutors or practice now 6th grade math worksheets.

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Power of Fractions - Grade 6 Math Worksheet PDF

This is a free printable / downloadable PDF worksheet with practice problems and answers. You can also work on it online.

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Let us just refresh our memory on the rules of exponents and importantly focus on the ‘Fraction rule’ before we go further.

What are the Rules for Exponents?

An Exponent is a short version of expressing how many times a number is supposed to be multiplied by itself.

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Solving Fractions with Exponents

Just like integers with exponent powers, we solve fractions with exponent powers.

Now, Let’s take a look at this example:

$\left ( \frac{2}{{3}} \right )^3$ = $\frac{2}{3}$ x $\frac{2}{3}$ x $\frac{2}{3}$ = $\frac{8}{27}$

How to solve this one?

The numerators get multiplied by itself and the denominators get multiplied by itself.

$\left ( \frac{4}{{7}} \right )^2$ = $\frac{4\ast4}{7\ast7}$ = $\frac{16}{49}$

Examples

$\left ( \frac{1}{{3}} \right )^3$ = $\frac{1}{3}$ x $\frac{1}{3}$ x $\frac{1}{3}$
$\left ( \frac{2}{{5}} \right )^4$ = $\frac{2}{5}$ x $\frac{2}{5}$ x $\frac{2}{5}$ x $\frac{2}{5}$ = $\frac{16}{625}$

Solving Fraction Exponents

$\frac{1}{2}$ as an exponent means square root.

$\frac{1}{3}$ as an exponent means cube root.

$\frac{1}{4}$ as an exponent means fourth root and so on.

Example

$(9)^{\frac{1}{2}}$ = $\sqr{9}$ = 3

$(343)^{\frac{1}{3}}$ = $\sqrt[3]{343}$ = 7

$(16)^{\frac{1}{4}}$ = $\sqrt[4]{16}$ = 2

$(8)^{\frac{4}{3}}$ = $\left ( 2 ^{3} \right )^{\frac{4}{3}}$ = $2^4$ = 16

Do You Stack Up Against the Best?

If you have 30 minutes, try our free diagnostics test and assess your skills.

Free Diagnostic Test for 6th Grade

Check Point

Solve the following:

1. $\left ( \frac{5}{9} \right )^2$

2. $\left ( \frac{3}{5} \right )^3$

3. $(81)^{\frac{1}{4}}$

4. $(256)^{\frac{5}{8}}$

5. $\left ( \frac{243}{32} \right )^{\frac{2}{5}}$

Answer key

1. $\frac{25}{81}$

2. $\frac{27}{125}$

3. 3

4. 32

5. $\frac{9}{4}$

Gloria Mathew writes on math topics for K-12. A trained writer and communicator, she makes math accessible and understandable to students at all levels. Her ability to explain complex math concepts with easy to understand examples helps students master math. LinkedIn

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