Printable Exponent Worksheets For Math Easy Squares and Cubes

There are eighteen third grade printable exponents worksheets on this page.

Squares and cubes are easy!

They teach raising a base number to different powers like the squares and cubes from different perspectives.

You can teach kids to memorize the squares and cubes, to learn the powers of ten as a base, and how to simplify exponents.

  1. Definition and using simple exponents with squares.
  2. Finding the square roots - a very similar exercise.
  3. Square roots charts.
  4. Square roots exponents with exponent charts.
  5. Cube exponent worksheets with exponent charts.
  6. Cube volume worksheets.
  7. PEMDAS order of operations.
  8. Exponents Video.
  9. Exponents Laws.

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1. Beginner Square Exponent Worksheets

Simple Exponent Definition And Explanation

Definition of an exponent from our Math Dictionary

  • Exponent - a little number to the right and a bit above a number; an expression of the number of times that a base is used as a factor.

This little number is a superscript. The exponent worksheets on this page introduce the visual element of the square of a base number (n2) which is the basis of learning square roots and also cubes (n3). 

Learning the squares is also the basis for how to figure square footage - simply multiply - the simplest math area formula.

Side x Side = Area = Square Footage

The square root of a number is a number that multiplies itself to solve exponents equations:

s x s = s2

2 x 2 = 4

By multiplying the expression 2 x 2 the factors can be expressed as 22 or 4.

Use this first worksheet for memory work to memorize the square exponents and use the other two as quizzes.

The bottom left exponent activity is way too difficult for some children to draw the lines, yet trying the first few can help them comprehend making a number square.

1.A. Squares Exponents Worksheet With Answers

This is the page to use while teaching the children to memorize the multiplication squares and to write the square superscript 2. (52, 62, 72).

It is an easy practice quiz preparation, too.

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1.B. Squares Exponents Quiz Worksheet

This page has the answer missing for an actual quiz. 

1.C. Making Squares

Use this page when older kids do not comprehend. It's actually quite a large project to draw all the lines, so allow plenty of time. I wouldn't use this worksheet with small children.

1.D. Making Squares - Fill In The Exponent

Use this page to show the relation between squares and the square roots. Ask "What squared equals one? What squared equals four? It's really a matter of asking the equation differently.

You can use these worksheets with Crewton Ramone's excellent video below. See also a link to his site where he explains the basics at the bottom of this page. 

He has worked for over twenty-five years as a professional math tutor, and has put his successful tutoring videos online. See his video below our printables for easy ways to teach square numbers using base ten blocks for exponents and multiplication.

Kids "see" squares and cubes "at-a-glance".

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2. 4 Simple Square Root Exponent Worksheets

Having a squares chart seems to be the only real square root formula.

If you memorize the squares (the doubles in multiplication), you'll recognize the factors when you are asked for the roots and you'll know most of the squares table for the elementary school grades.

These worksheets can be skipped if your kids understand that square roots "undo" or invert the square equation like division is the inverse of multiplication, like products and quotients.

SPECIAL NOTE: The radicand symbol is simply the division symbol with the left entry crossed out. No need to write it as it is the same number.

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3. Printable Exponent Charts: Second, Third And Fourth Powers

3.A. Adding Exponents

Every natural number has an exponent or power of one.

  • 11, 21, 31, 41, 51, ....

If we multiply a number by itself we add the exponents the number of times we multiply. You can see this at a glance in the printable exponents charts below. Children often understand easily when they see the chart for squares and cubes.

Adding Squared Exponents

Squares are numbers multiplied to the second power, so the expanded form expression is

31 x 31 = 32 = 9

In English this equation reads as 

"Three times three are three squared or nine".

This principle is so helpful for showing that the area of a square uses the same math facts as multiplication and the formula for making squares.

s x s = Area

Adding Cubed Exponents

It is similar for cubes. Cubes are numbers multiplied to the third power, so in expanded form

31 x 31 x 31 = 33 = 27

In English this equation reads as: 

"Three times three times three are three cubed or twenty-seven."

The three 1 exponents are added to equal an exponent of 3.

This proves that  the volume of a cube uses the same factors as multiplication and the formula for making cubes.

s x s x s = Cube

Exponent addition is so much easier to see with the following printable charts.

Additive Properties Of Exponents In Advanced Math

This is really so simple when you realize that any number n,

n2 x n3 is n5.

It's one of the laws of exponents.

3.B. Square Roots Charts To Print

Have you ever tried finding an exponent chart? Or needed a square root table?

They can be hard to find, so

  • we have made an exponents chart for you to use as a math poster or to put in your binder for reference.
  • We've also made handy little cards to cut and share. 

Use these exponents worksheets to practice the multiplication facts necessary to find the squares and cubes.

Cube worksheets are below and use the same chart as these square worksheets. The charts go as high as the fourth power, n4.

The next printable exponent chart has four of the first one and can be cut to use as a bookmark in a math book or kept in a desk, binder, or taped in a math textbook.

3.C. Square Roots Rules of Exponents

The formula for square roots is the inverse of the formula of a square, or the area of a square; yet in reverse like dividing.

Using an exponents chart makes the powers easy to see.

One of the rules of exponents:

  • REMEMBER that, when working in reverse from square to root, the answer to solving the square root can be negative or positive. 
  • 32 or 9 can be both 3 x 3 or -3 x -3
  • Three squared, or nine, can be three times three or negative three times negative three.

3.D. Printable Exponents Chart To The Fourth Power And Base 12

Keep this printable exponents chart in your binder or on the wall next to your desk. It covers the exponentional powers to 4.

The columns show the powers and the rows show the bases. A common base is base ten. That means that the base number is ten to the power of 2, 3, or 4, etc.

  • Roman numeral C is an exponent of X where ten is X and one hundred: is C. See more about Roman numerals here.
  • Metric measurement is an excellent example of base ten expressions.
  • In counting money pennies, dimes, dollars, and ten dollar bills we use powers of ten.
  • Scientific notation and measurement in math, engineering, and chemistry depend on base ten.

If you have the children memorize the 2s, 5s and 10s, those squares, cubes, and square roots will be easy to solve in basic math class and simplifying expressions with exponents in 5th and 6th grade or pre-algebra where they will have to evaluate expressions that have exponents.

Over time kids will begin to see patterns.

3.E. Printable Exponents Charts To The Power Of 4

These printable exponents charts print four-up for classroom handouts or math bookmarks. Make several copies to share.

I gave one to each child to tape to the inside of their math books for easy reference. Super helpful with square roots!

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4. Square Exponent Worksheets With Exponent Chart

These first two worksheets are great practice because the exponential equations are right on the page.

  1. The first practice worksheet shows how to get from squares to cubes with the squares already figured.
  2. The second worksheet has blanks to figure the squares. When you square a number the second number is the same as the first.

The final answer can be written as a superscript or the multiplied answer.

4.A. Multplying Squares With Exponents Chart

4.B. Multplying Squares With Exponents Chart Worksheet

4.C. Find The Area Of A Square Exponent Worksheet

4.D. Find The Area Of Square Inches Exponents Worksheet

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5. Cube Exponent Worksheets With Exponent Charts

5.A. Cube Exponent Worksheets With Exponent Chart

Again, practice the equation which can be copied from the equations on the page. These worksheets spell out the square and cube relationships directly.

  1. The first practice worksheet shows how to get from squares to cubes with the squares already written. 
  2. The second worksheet has blanks to figure both the squares and the cubes. 

5.B. Cube Exponent Worksheet With Exponent Chart

5.C. Blank Cube Exponent Worksheet With Exponent Chart

Beginner Volume Of A Cube Word Problems

These two printable exponent worksheets can help a child visualize the words that we use to talk about the cube roots. Use the square root table above to find the cube root since both are on the table. A cube's volume is simply the height times the width times the base sides.

h x w x b = Volume

If the cube is a square cube, the sides are all equal and when multiplied give the volume of a cube.

s x s x s = Volume

It is a giant help to show young children what a cube looks like with Math manipulatives or a Rubics cube.

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6. Cube Volume Worksheets

Use these exponent worksheets for square cubes.

Also teach that the real exponent for the first number is 1, so the exponents add up to 3 for cubes: 1+2=3.

6.A. Cube Volume Worksheet #1

6.A. Cube Volume Worksheet #2

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7. Exponents And PEMDAS

First, make certain that your students are relatively handy with multiplication and division. The better your students know their math facts, the easier it will be for them to learn exponents. 

If your students aren't handy and need practice, use our fun multiplication worksheets, then come back to this page.

Exponents are simply multiplication, and square roots are tricky division. It helps to have a chart for the roots which is why we include the charts in the worksheets above.

Exponents come second in the order of operations for Pre-Algebra. Use this phrase to remember the order: "Please excuse my dear Aunt Sara." or use the phrase PEMDAS and pronounce it as a word, Pemdas.

Negative exponents mean the reciprocal of the base raised to the power of the exponent. They wind up being fractions or division.

Practice is necessary to gain speed using exponents. Knowing how to use and find exponents well makes learning math and science so much easier!  See our Order of Operations Worksheets to offer practice using PEMDAS. 

You might also like our handy geometry formula sheet.

8. Crewton Ramone's Math Exponents Video - Squares

See more excellent videos on Square Numbers at Crewton Ramone's House Of Math square numbers. He's one tutor that's got a wonderful talent for teaching Math. Sign up for his Password to see more info.

9. Exponent Laws Or Rules Of Exponents

The basic exponent laws are:

  1. The exponent tells how many times to multiply the number.
  2. If the exponent is 0 the simplified answer is 1.
  3. Negative exponents are signs for dividing.

MathsIsFun has a great explanation of the laws of exponents.

10. Maria Miller's Math Mammoth

You will love Maria Miller's Math Mammoth worktexts and worksheets. She explains everything in order and super well.

Find Math Mammoth at Amazon.

11. More Printable Math Worksheets

We have hundreds of practice math worksheets.

Printable Worksheets By Grade

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Mary Fifer
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Mary is webmaster at PrintNPractice.com and created elementary school practice exercises using digital interactive worksheets. Printable and perfect for today's teachers, tutors, homeschoolers, and students!

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