5th Grade - Powers And Exponents

Numbers - Small, Large and Prime
Powers and Exponents
Understand and compute positive integer powers of nonnegative integers; compute examples as repeated multiplication.
Students need to know what exponents are, that they represent repeated multiplication, and be able to solve simple problems using exponents

Sample Problems


When is it useful to use repeated addition? (when you want to multiply)


Solve: 5x5x5 (125)


Write using exponents: 3x3x3x3x3x3x3 (3^7)


Write in expanded form: 9 squared (9x9)


Solve: 6 cubed (6x6x6)

Learning Tips


It is helpful for kids to understand why something times itself is called squared. If you draw a picture of a square and show that both the length and height are the same, they will remember it is squared.


In the same respect, you can show kids something times itself, times itself again is cubed. Draw a picture of a cube and show that the length, height and width are all the same. Compare this to 3D too. Students understand this connection much easier once they have completed the geometry standards for 5th grade.


One of the great mysteries of 5th grade math is why students, even when they understand exponents, choose that 35 is 3x5 on a multiple choice test. As a teacher, I demand that my students work out their exponent problems to see for themselves that this is incorrect. Expect that your child will make the same mistake, and with enough repetition, the idea eventually sticks.


I often remind my students of the “good ol’ days” back in 3rd grade when they were learning that multiplication is repeated addition. They used to have races on the board: one side adding 4+4+4+4+4 and the other 4x5. They see that the multiplication saves time. The same idea applies to repeated multiplication and exponents. One side multiplied 6x6x6 and the other did 63. Since this was building on something they already experienced, they understood fairly quickly.


Exponential growth, while it is not directly taught in 5th grade, is still a basic idea students can play around with. 10 and 11 year olds still think of calculators as toys instead of tools, so allowing your child “play time” to see what 7612 looks like on the calculator is entertaining and educational.

Extra Help Problems


Write in expanded form: 79 (7x7x7x7x7x7x7x7x7)


Write in expanded form:86 (8x8x8x8x8x8)


Write in expanded form: 203 (20x20x20)


Write in expanded form:145 (14x14x14x14x14)


Write in expanded form: 356 (35x35x35x35x35x35)


Write in expanded form: 425 (42x42x42x42x42)


Write in expanded form: 124 (12x12x12x12)


Write in expanded form: 187 squared (187x187)


Write in expanded form: 673 cubed (673x673x673)


Write in expanded form: 97362 (9736x9736)


Write using exponents: 6x6x6 (6^3)


Write using exponents: 4x4x4x4x4x4x4 (4^7)


Write using exponents: 8x8 (8^2)


Write using exponents: 21x21x21x21 (21^4)


Write using exponents: 59x59x59 (59^3)


Write using exponents: 38x38x38x38x38 (38^5)


Write using exponents:213x213 (213^2)


Write using exponents:379x379x379x379x379x379 (379^6)


Write using exponents: 621x621x621 (621^3)


Write using exponents: 72,918 x 72,918x72,918 (72,918^3)


Solve: 9 squared (81)


Solve: 35 (243)


Solve: 4 cubed (64)


Solve: 54 (625)


Solve: 26 (64)


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