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Rules of Rules of ExponentsExponents
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IntroductionIntroduction
Product Rule—when Product Rule—when multiplyingmultiplying with the same base, with the same base, addadd exponents. exponents.
Quotient Rule—when Quotient Rule—when dividingdividing with with the same base, the same base, subtractsubtract exponents. exponents.
Power Rule—when Power Rule—when raising a power raising a power to a powerto a power, , multiplymultiply exponents. exponents.
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Goal: Multiply PowersGoal: Multiply Powers To multiply powers with To multiply powers with
the same base, add their the same base, add their exponents.exponents.
aamm • a • ann = a = am + nm + n
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Guided PracticeGuided PracticeFind the product. Write your answer using exponents.Find the product. Write your answer using exponents.
4477 • 4 • 41111
447 + 117 + 11 = 4 = 41818
2255 • 2 • 21212
225 + 125 + 12 = 2 = 21717
5566 • 5 • 52 2 • 5• 533
556 + 2 + 36 + 2 + 3 = = 551111
xx66 • • xx1313
xx6 + 13 6 + 13 = = xx1919
bb22 • • bb4 4 • • bb bb2 + 4 + 1 2 + 4 + 1 = = bb77
22xx2 2 • 7• 7xx66
2 • 7 • 2 • 7 • xx2 + 62 + 6
1414xx88
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Independent PracticeIndependent PracticeFind the product. Write your answer using exponents.Find the product. Write your answer using exponents.
1. 51. 51010 • 5 • 51111
2. 42. 488 • 4 • 499
3. 53. 544 • 5 • 533
4. 4. nn88 • • nn99
5. 5. yy1010 • • yy1212
6. (-6. (-aa))88 • (- • (-aa))99
7. 67. 677 • 6 • 62 2 • 6• 688
8. 8. dd44 • • dd88
9. 39. 3hh55 • 4 • 4hh6 6
10. 510. 5gg2 2 • • gg1616
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Goal: Divide PowersGoal: Divide Powers To divide powers with the To divide powers with the
same base, subtract their same base, subtract their exponents.exponents.
aamm = a = am - nm - n
a ann
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Guided PracticeGuided PracticeFind the quotient. Write your answer using exponents.Find the quotient. Write your answer using exponents.
441111
4477
4411 – 7 11 – 7 = 4= 444
221212
2255
2212 – 512 – 5 = 2 = 277
xx99 xx33
xx9 – 3 9 – 3 = = xx66
xx1313 xx33
xx13 – 3 13 – 3 = = xx1010
bb44 bb
bb4 – 1 4 – 1 = = bb33
3535xx6 6
77xx22
35 35 7 7 xx6 –26 –2
55xx44
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Independent PracticeIndependent PracticeFind the quotient. Write your answer using exponents.Find the quotient. Write your answer using exponents.
1. 1. 4499
4477
2. 2. 221212
2255
3. 3. xx99 xx33
4. 4. xx1313 xx33
5. 5. yy2020 yy1212
6. 6. bb44 bb
7. 7. 4949xx5 5
77xx22
8. 8. 2525xx6 6
55xx9. 9. 3636xx8 8
99xx33
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Goal: Raise a power to a Goal: Raise a power to a powerpower
To raise a power to a To raise a power to a power, multiply their power, multiply their exponents.exponents.
(a(amm))nn = a = am • nm • n
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Guided PracticeGuided PracticeFind the power. Write your answer using exponents.Find the power. Write your answer using exponents.
(4(477))1111
447 7 •• 11 11 = 4 = 47777
(2(255))1212
225 5 •• 12 12 = = 226060
(5(566))22
556 6 •• 2 2 = 5 = 51212
((xx66))33
xx6 6 •• 3 3 = = xx1818
((bb22))-4-4
bb2 2 •• -4 -4 = = bb-8 -8 = = 1/b1/b88
((xx-2-2))-3-3
xx-2 -2 •• -3 -3 = = xx66
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Independent PracticeIndependent PracticeFind the power. Write your answer using exponents.Find the power. Write your answer using exponents.
1. (51. (51010))22
2. (42. (488))33
3. (53. (544))33
4. (4. (nn88))22
5. (5. (yy1010))-2-2
6. (6. (aa-5-5))-8-8
7. (67. (677))88
8. (8. (dd44))-8-8
9. (9. (hh-5-5))-6 -6
10. (10. (gg22))1616
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SummarySummary
Product Rule—when Product Rule—when multiplyingmultiplying with the same base, with the same base, addadd exponents. exponents.
Quotient Rule—when Quotient Rule—when dividingdividing with with the same base, the same base, subtractsubtract exponents. exponents.
Power Rule—when Power Rule—when raising a power raising a power to a powerto a power, , multiplymultiply exponents. exponents.