INTEGER EXPONENTS HOMEWORK. 1. For each of the following, determine the integer value of n that satisfies the equation. The first is done for you.

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1 Name: Date: INTEGER EXPONENTS HOMEWORK Algebra II INTEGER EXPONENTS FLUENCY. For each of the following, determine the integer value of n that satisfies the equation. The first is done for ou. n = 8 n = n = n = (b) n = 6 (c) n = (d) 7 n = 8 n = (f) 0 n = (g) n = 0, 000 (h) n =. Use the Addition Propert of Eponents to simplif each epression. Then, find a final numerical answer without using our calculator. (b) 7 0 (c) Use the Product Propert of Eponents to simplif each eponential epression. You do not need to find a final numerical answer. ( ) ( ) (b) ( ) (c) ( ) COMMON CORE ALGEBRA II, UNIT # EXPONENTIAL AND LOGARITHMIC FUNCTIONS LESSON # emathinstruction, RED HOOK, NY 7, 0

2 . The eponential epression 8 is equivalent to which of the following? Eplain our choice. () () 8 () 8 () REASONING. How can ou use the fact that = 6 to show that =? Eplain our process of thinking We've etended the two fundamental eponent properties to negative as well as positive integers. What would happen if we etended the Product Eponent Propert to a fractional eponent like? Let's pla around with that idea. Use the Product Propert of Eponents to justif that ( 9 ) = 9. (b) What other number can ou square that results in 9? Hmm... COMMON CORE ALGEBRA II, UNIT # EXPONENTIAL AND LOGARITHMIC FUNCTIONS LESSON # emathinstruction, RED HOOK, NY 7, 0

3 FLUENCY RATIONAL EXPONENTS HOMEWORK. Rewrite the following as equivalent roots and then evaluate as man as possible without our calculator. 6 (b) 7 (c) (d) 00 6 (f) 9 (g) 8 (h). Evaluate each of the following b considering the root and power indicated b the eponent. Do as man as possible without our calculator. 8 (b) (c) 6 (d) 8 (f) 7 8 (g) 6 (h). Given the function ( ) ( ) f = +, which of the following represents its -intercept? () 0 () () 0 () 0 COMMON CORE ALGEBRA II, UNIT # EXPONENTIAL AND LOGARITHMIC FUNCTIONS LESSON # emathinstruction, RED HOOK, NY 7, 0

4 . Which of the following is equivalent to () () () ()?. Written without fractional or negative eponents, () () () () is equal to 6. Which of the following is not equivalent to () 096 () 6 6? () 8 () 6 7. Which of the following is equivalent to? () () () () 8. If the epression was placed in a form, then which of the following would be the value of a? () () () () COMMON CORE ALGEBRA II, UNIT # EXPONENTIAL AND LOGARITHMIC FUNCTIONS LESSON # emathinstruction, RED HOOK, NY 7, 0

5 9. Which of the following is not equivalent to 9? () () 9 () ( ) 9 () 0. If the function = was placed in the form a b = then which of the following is the value of ab? () 6 () 6 () (). Rewrite each of the following epressions without roots b using fractional eponents. (b) (c) 7 (d) (f) (g) (h) 9. Rewrite each of the following without the use of fractional or negative eponents b using radicals. 6 (b) 0 (c) (d) (f) 7 (g) 9 (h) COMMON CORE ALGEBRA II, UNIT # EXPONENTIAL AND LOGARITHMIC FUNCTIONS LESSON # emathinstruction, RED HOOK, NY 7, 0

6 REASONING. Marlene claims that the square root of a cube root is a sith root? Is she correct? To start, tr rewriting the epression below in terms of fractional eponents. Then appl the Product Propert of Eponents. a. We should know that 8 =. To see how this is equivalent to do this, we can rewrite the equation as: n = ( ) How can we now use this equation to see that 8 =? 8 = we can solve the equation 8 n =. To. Mikala was tring to rewrite the epression in an equivalent form that is more convenient to use. She incorrectl rewrote it as. Eplain Mikala's error. COMMON CORE ALGEBRA II, UNIT # EXPONENTIAL AND LOGARITHMIC FUNCTIONS LESSON # emathinstruction, RED HOOK, NY 7, 0

7 EXPONENT PRACTICE HOMEWORK FLUENCY. Rewrite each of the following epressions in simplest form and without negative eponents. 7 ( ) (b) 0 (c) ( ( ) ) (d) ( ) 8. Which of the following represents the value of a when a = and b =? b () 9 () 6 () 8 (). Simplif each epression below so using radicals. that it contains no negative eponents. Do not write the epressions 7 ( (b) ) (c) ( )( ). Which of the following represents the epression () () 6 written in simplest form? () () COMMON CORE ALGEBRA II, UNIT # EXPONENTIAL AND LOGARITHMIC FUNCTIONS LESSON # emathinstruction, RED HOOK, NYY 7, 0

8 . Which of the following is equivalent to 0? () () () () 6. When written in terms of a fractional eponent the epression 7 () () is () () 7. Epressed as a radical epression, the fraction () 6 () 6 () 6 () 6 is COMMON CORE ALGEBRA II, UNIT # EXPONENTIAL AND LOGARITHMIC FUNCTIONS LESSON # emathinstruction, RED HOOK, NY 7, 0

9 Answers to Integer Eponents Homework. n = - (b) n = (c) n = - (d) n = 0 n = - (f) n = - (g) n = 0 (h) n = -.. = (b) (b) 0 = (c) or. (). show steps 6. show steps (b) (c) 0 6 = 00 Answers to Rational Eponents Homework. 6 = 6 (b) 7 = (c) 6 = (f) 9 = 7 (g). (b) 8 (c) 8 (d) (f) 8 (g) (h) 7. () 8. (). () 9. (). () 6. () 0. () 7. (). (b) (f) (c) (g). 6 (b) 0 (c) (f) 7 = (d) 0 00 = 8 = (h) = 7 7 (d) (g) 9 (h) 9 (h) (d). es show wh. show steps. she took the square root of, which is not being raised to the ½ power COMMON CORE ALGEBRA II, UNIT # EXPONENTIAL AND LOGARITHMIC FUNCTIONS LESSON # emathinstruction, RED HOOK, NY 7, 0

10 Answers to Eponent Practice Homework. (b) (c) 6. ().. (). () 6. () 7. () (b) (c) (d) 8 COMMON CORE ALGEBRA II, UNIT # EXPONENTIAL AND LOGARITHMIC FUNCTIONS LESSON # emathinstruction, RED HOOK, NY 7, 0