Numbers 4 1 Algebra a 1 where a 0 Negative Exponents Words For any integer n

# Numbers 4 1 algebra a 1 where a 0 negative exponents

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Numbers 4 0 = 1 Algebra a 0 = 1, where a 0 Negative Exponents Words For any integer n and any nonzero number a , a n is the reciprocal of a n . Numbers 4 2 = 1 4 2 Algebra a n = 1 a n , where a 0
Section 6.1 Properties of Exponents 293 Using Properties of Exponents Simplify each expression. Write your answer using only positive exponents. a. 3 2 3 6 b. ( 4) 2 ( 4) 7 c. ( z 4 ) 3 SOLUTION a. 3 2 3 6 = 3 2 + 6 Product of Powers Property = 3 8 = 6561 Simplify. b. ( 4) 2 ( 4) 7 = ( 4) 2 7 Quotient of Powers Property = ( 4) 5 Simplify. = 1 ( 4) 5 = 1 1024 Definition of negative exponent c. ( z 4 ) 3 = z 4 ( 3) Power of a Power Property = z 12 Simplify. = 1 z 12 Definition of negative exponent Monitoring Progress Help in English and Spanish at BigIdeasMath.com Simplify the expression. Write your answer using only positive exponents. 5. 10 4 10 6 6. x 9 x 9 7. 5 8 5 4 8. y 6 y 7 9. (6 2 ) 1 10. ( w 12 ) 5 Using the Properties of Exponents Core Concept Product of Powers Property Let a be a real number, and let m and n be integers. Words To multiply powers with the same base, add their exponents. Numbers 4 6 4 3 = 4 6 + 3 = 4 9 Algebra a m a n = a m + n Quotient of Powers Property Let a be a nonzero real number, and let m and n be integers. Words To divide powers with the same base, subtract their exponents. Numbers 4 6 4 3 = 4 6 3 = 4 3 Algebra a m a n = a m n , where a 0 Power of a Power Property Let a be a real number, and let m and n be integers. Words To fi nd a power of a power, multiply the exponents. Numbers (4 6 ) 3 = 4 6 3 = 4 18 Algebra ( a m ) n = a mn REMEMBER The expression x 3 is called a power . The base , x , is used as a factor 3 times because the exponent is 3.
294 Chapter 6 Exponential Functions and Sequences Using Properties of Exponents Simplify each expression. Write your answer using only positive exponents. a. ( 1.5 y ) 2 b. ( a 10 ) 3 c. ( 3 d 2 ) 4 d. ( 2 x 3 ) 5 SOLUTION a. ( 1.5 y ) 2 = ( 1.5) 2 y 2 Power of a Product Property = 2.25 y 2 Simplify. b. ( a 10 ) 3 = a 3 ( 10) 3 Power of a Quotient Property = a 3 1000 Simplify. c. ( 3 d 2 ) 4 = (3 d ) 4 2 4 Power of a Quotient Property = 3 4 d 4 2 4 Power of a Product Property = 81 d 4 16 Simplify. d. ( 2 x 3 ) 5 = (2 x ) 5 3 5 Power of a Quotient Property = 3 5 (2 x ) 5 Definition of negative exponent = 3 5 2 5 x 5 Power of a Product Property = 243 32 x 5 Simplify. Monitoring Progress Help in English and Spanish at BigIdeasMath.com Simplify the expression. Write your answer using only positive exponents. 11. (10 y ) 3 12. ( 4 n ) 5 13. ( 1 2 k 2 ) 5 14. ( 6 c 7 ) 2 ANOTHER WAY Because the exponent is negative, you could find the reciprocal of the base first. Then simplify.

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