This document provides a review of the 5 basic rules of exponents through examples and explanations of each rule. It includes review exercises with solutions for each rule covering: multiplying different integers with exponents, dividing with equal exponents, raising exponents to exponents, multiplying equal integers with exponents, and dividing with unequal exponents. Videos and additional resources are also provided for further review of exponents.

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2. In class, we have been learning about

the 5 basic rules of exponents for the last
few weeks. This activity should be used
as a review, that is, all students should be
familiar with these rules, and know how
to solve these types of problems. In this
activity you will find review
exercises, with full solutions, and also
some fun video links to check out!
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3. For additional review, take a look at this!

› Exponent Review Video
Rule 1: Multiplying Different Integers with Exponents

Rule 2: Dividing with Equal Exponents

Rule 3: Raising Exponents to Exponents

Rule 4: Multiplying Equal Integers with Exponents

Rule 5: Dividing with Unequal Exponents

Check out this song!

About Me

Resources

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4. This rule states that when we have two

integers raised to different powers, we
simply add the exponents.
 Try these:
› 63x67= ?
› 45x42= ?
Click the ? for the solutions!
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5. › Remember, we just add the exponents when
the bases are the same!
› 63x67 = 6(3+7) = 610 = 60,466,176
› 45x42 = 4(5+2) = 47 = 16,384
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6. This rule states that when one integer

raised to a power divided by a different
integer raised to the same power, we
simply divide the integers and raise the
quotient to the power.
 Try these:
› 76/26 = ?
› 23/93 = ?
Click the ? for the solutions!
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7. › Remember, we just divide the bases
when the exponents are the same!
› 76/26 = (7/2)6 = (3.5)6 ≈ 1838.266
› 23/93 = (2/9)3 ≈ (.22222)3 ≈ 0.010974
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8. This rule states that if one integer is raised

to one power, and this is raised to a
power, we simply raise the integer to the
products of the powers.
 Try these:
› (33)6 = ?
› (54)2 = ?
Click the ? for the solutions!
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9. › Remember, we just multiply the
powers!
› (33)6 = 33x6 = 318 = 387,420,489
› (54)2 = 54x2 = 58 = 390,625
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10. This rule states that if we have two

different integers raised to the same
power, we simply multiply the integers
and raise the product to the power.
 Try these:
› 8242 = ?
› 5474 = ?
Click the ? for the solutions!
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11. › Remember, we just multiply the
bases and raise the product to the
power!
› 8242 = (8x4)2 = 322 = 1024
› 5474 = (5x7)4 = 354 = 1,500,625
Quiz

12. This rule states that if we have one

integer raised to a power divided by the
same integer raised to a different
power, we simply find the difference of
the powers and raise the integer to this
difference.
 Try these:
› 58/53 = ?
› 69/66 = ?
Click the ? for the solutions!
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13. › Remember, we just find the
difference of the powers and raise
the base to the power!
› 58/53 = 5(8-3) = 55 = 3125
› 69/66 = 6(9-6) = 63 = 216
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14. Hello! My name is Katie

Lantz and I am a
sophomore at Grand
Valley State University. I
am majoring in
mathematics and
minoring in
psychology, and I hope
to become a high
school math teacher
some day soon!
Email me with questions

or comments! Quit

15. Review Video

› http://www.youtube.com/watch?v=0ykBpa
pHaCU
Exponents Song

› http://www.youtube.com/watch?v=xwWmd
zfV_Uk&feature=PlayList&p=4BC7A2AF721C5
198&index=2
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