Rules of Rules of ExponentsExponents

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.

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

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

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

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

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

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

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

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

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

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.