7-1: Zero and Negative Exponents

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1 7-: Zero nd Negtive Exponents Objective: To siplify expressions involving zero nd negtive exponents Wr Up:.. ( ) Investigting Zero nd Negtive Exponents: Coplete the tble. Write non-integers s frctions in siplest for. Exponent, n Power, n Power, n Power, n Wht ppers to be the vlue of 0 for ny nuber? How cn you evlute n expression of the for n? Zero nd Negtive Exponent Properties: 0 n

2 Exple : 0 (.) 0 d) 7 e) ( ) f) Exple : x b c d d) k e) 9 8 7n f) y ( ) Exple : Evlute ech expression without using clcultor. for nd b b x y for x nd y Exple : The popultion of puppies doubles every onth. The expression 000 odels popultion of 000 puppies fter onths of growth. Evlute for 0 nd. Describe wht the vlue of the expression represents in the sitution. Closure Question: Wht is the first step for siplifying n exponentil expression tht contins negtive exponents?

3 7- & 7-: Multipliction Properties of Exponents Objective: To ultiply powers with the se bse To rise power to power nd product to power Wr Up: c. 9 n 8 Investigting Multipliction of Exponents: 7 7 x x Wht pttern do you notice? x Wht pttern do you notice? 8 x y Wht pttern do you notice? Multipliction Properties of Exponents: n n b

4 different Exple : Rewrite ech expression using ech bse only once. e 8 e Exple : 7 c c c x y x y Exple : b 8b 7 n n Exple : z 7 d d k k Exple : p g h u v 7 Exple : x y xy 7c d c d Closure Question: How is siplifying n thn siplifying n?

5 7-: Division Properties of Exponents Objective: To divide powers with the se bse To rise quotient to power Wr Up: c c 7 7. x y x y Investigting Division of Exponents: x x 7 Wht pttern do you notice? 9 x y Wht pttern do you notice? Division Properties of Exponents: n b

6 Exple : g g ( ) ( ) 7 7 n n 8 9 Exple : 0 x y z x y z 9 b c b c Exple : n 9 c d e c d e d) xy x y z Closure Question: How is dividing powers with the se bse different fro ultiplying powers with the se bse?

7 7-: Rtionl Exponents nd Rdicls Objective: To rewrite expressions involving rdicls nd rtionl exponents Wr Up: c 8 9. g g. 0 n. u v u v. x y z x y z Equivlence of Rtionl Exponents nd Rdicls: b n Exple : 9 Exple : Write ech expression in siplified rdicl for. 7 (8 x )

8 Exple : Write ech expression in siplified exponentil for. 9 g 8 n 7y Exple : Siplify ech expression using the properties of exponents. Then write the expression in rdicl for. 7 0 h h 0 c d z z Exple : Siplify ech expression using the properties of exponents nd without using clcultor x y Exple : You cn estite the etbolic rte of living orgniss bsed on body ss using Kleiber s lw. The forul R 7. M reltes etbolic rte R esured in clories per dy to body ss M esured in kilogrs. Wht is the etbolic rte of dog with body ss of 8 kg? Closure Question: n In the expression b, which vrible is the power nd which vrible is the root?

9 0-: Siplifying Rdicls Objective: To siplify rdicls involving products nd quotients Wr Up: Identify Perfect Squres: Investigting Properties of Rdicls: Evlute the rdicl expressions b nd b for the given vlues of nd b. ), b 9 ), b 00 ), b Wht cn you conclude? Evlute the rdicl expressions b nd for the given vlues of nd b. b ) 8, b 9 ), b ), b Wht cn you conclude? Properties of Rdicls: b b A rdicl expression is in SIMPLEST FORM if the following re true: The rdicnd hs no perfect squre fctors other thn. The rdicnd hs no frctions. The denointor of frction hs no rdicl.

10 Exple : Siplify ech rdicl expression d) 8 Exple : Siplify ech rdicl expression. x 98 c n Exple : Siplify ech rdicl expression. 0 8 d d Exple : Siplify ech rdicl expression y 0h h Exple : You cn use the forul d.h to estite the distnce d in iles to horizon when h is the height of the viewer s eyes bove the ground in feet. Suppose you re looking out fourth floor window feet bove ground. Estite the distnce you cn see to the horizon. Round your nswer to the nerest ile. Closure Question: Explin how to siplify rdicl.

11 0-: Opertions with Rdicl Expressions Objective: To siplify rdicl expressions involving,,, Wr Up: Siplify ech rdicl expression x y. 98c. 7 n Cobining Like Rdicls: Like rdicls hve the se rdicnd: 8, 9 8 Unlike rdicls do not hve the se rdicnd:, Exple : Siplify ech rdicl expression. 8 0 Exple : Siplify ech rdicl expression. 7 8

12 Exple : Siplify ech rdicl expression. ( 8) 7 ( 7 ) Exple : Siplify ech rdicl expression. (7 0) 8 ( ) Closure Question: When cn you dd nd subtrct rdicl expressions?

13 0-: Solving Rdicl Equtions Objective: To solve equtions contining rdicls Wr Up: Evlute ech expression for the given vlue.. x for x =. x for x = 8. x for x = 7 Siplify ech expression.. 9. x. x 7 rdicl eqution: n eqution tht hs vrible in rdicnd Steps to Solve Rdicl Equtions: Get rdicl by itself on one side Squre both sides to cncel rdicl Solve for vrible Check your solution Exple : Solve ech rdicl eqution. Check your solution. x x Exple : Solve ech rdicl eqution. Check your solution. d d 8 n n 0

14 Exple : Solve ech rdicl eqution. Check your solution. c 8 7 z d) 0 Exple : On roller coster ride, your speed in loop depends on the height of the hill you hve just coe down nd the rdius of the loop in feet. The eqution v 8 h r gives the velocity v in feet per second of cr t the top of the loop. Suppose the loop hs rdius of 8 ft. You wnt the cr to hve velocity of 0 ft/sec t the top of the loop. How high should the hill be? Closure Question: How do you solve rdicl eqution?

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