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NAME DATE 7-2 PERIOD Study Guide and Intervention Division Properties of Exponents Divide Monomials To divide two powers with the same base, subtract the exponents. Quotient of Powers am m-n . For all integers m and n and any nonzero number a, − n = a Power of a Quotient a For any integer m and any real numbers a and b, b ≠ 0, − a (b) a 4b 7 Simplify − . Assume 2 Example 2 ab that no denominator equals zero. ( )( ) a 4b 7 a4 b7 − = − 2 a − ab b2 4-1 7-2 = (a )(b ) = a3b5 The quotient is a3b5. am =− m . b 3 2a 3b 5 Simplify − . Assume 2 ( 3b ) that no denominator equals zero. Group powers with the same base. 3 5 2 Quotient of Powers Simplify. 3 (2a 3b 5) 3 (3b ) 2 3(a 3) 3(b 5) 3 =− (3) 3(b 2) 3 8a 9b 15 =− 27b 6 8a 9b 9 =− 27 8a 9b 9 The quotient is − . 27 2a b (− 3b ) =− 2 3 Power of a Quotient Power of a Product Power of a Power Quotient of Powers Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Exercises Simplify each expression. Assume that no denominator equals zero. 55 3 5 or 125 1. − 2 5 m6 2. − m2 4 a2 4. − a a 5. − y 5 2 xy 6 yx (rw ) 2r 5w 3 10. − 4 3 Chapter 7 m x 5y 3 xy 6. −5 - −y 2 ( ) 2a 2b 8. − a y2 7. − 4 4 16r 4 p 5n 4 pn 3. − p3n3 2 3 ( 2r n ) 3r 6n 3 11. − 5 4 -2y 7 14y 8a3b3 81 16 − r 4n 8 11 ( ) 4p 4r 4 3p r 9. − 2 2 1 7 3 64 27 − p 6r 6 r 7n 7t 2 4 4 12. − rn 3 3 2 nrt Glencoe Algebra 1 Lesson 7-2 Example 1 m NAME DATE 7-2 Study Guide and Intervention PERIOD (continued) Division Properties of Exponents Negative Exponents Any nonzero number raised to the zero power is 1; for example, (-0.5)0 = 1. Any nonzero number raised to a negative power is equal to the reciprocal of the 1 . These definitions can be used to number raised to the opposite power; for example, 6 -3 = − 3 6 simplify expressions that have negative exponents. Zero Exponent For any nonzero number a, a0 = 1. Negative Exponent Property 1 1 n For any nonzero number a and any integer n, a -n = − n and − -n = a . a a The simplified form of an expression containing negative exponents must contain only positive exponents. -3 6 4a b . Assume that no denominator equals zero. Simplify − 2 6 -5 Example 16a b c -3 ( 16 )( a )( b )( c ) 6 -3 6 4a b b 4 a 1 − − − − = − 2 6 -5 2 6 -5 16a b c 1 =− (a -3-2)(b 6-6)(c 5) ( ) Quotient of Powers and Negative Exponent Properties Simplify. Negative Exponent and Zero Exponent Properties Simplify. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 4 1 -5 0 5 =− a bc 4 1 1 − (1)c 5 =− 4 a5 c5 =− 4a 5 c5 The solution is − . 4a 5 Group powers with the same base. Exercises Simplify each expression. Assume that no denominator equals zero. p -8 1 p p 22 25 or 32 1. − -3 m 2. − m5 -4 b -4 b 4. − -5 b −2 5. − -1 2 x 4y 0 x − 8. − 2 4 2 6 2 7. − x6 -2 1 m -3t -5 −2 10. − 2 3 -1 (m t ) Chapter 7 mt − 3. − 3 11 m (-x -1y) 0 w 4w y 4y 6. − a6 b8 -2 (6a -1b) 2 36 (b ) ab − 9. − -1 2 7 11 ( 8m ) 4m 2n 2 11. − -1 0 1 12 (a 2b 3) 2 (ab) (3rt) 2u -4 9r 3 r tu u (-2mn 2) -3 4m n m3 32n 12. − -− -6 4 10 Glencoe Algebra 1