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Math 010 - Cooley Elementary Algebra OCC Section 4.8 – Negative Exponents and Scientific Notation Negative Exponents For any real number a that is nonzero and any integer n, a n 1 an (The numbers a n and a n are reciprocals of each other.) Factors and Negative Exponents For any nonzero real numbers a and b and any integers m and n, a n b m b m a n (A factor can be moved to the other side of the fraction bar if the sign of the exponent is changed.) Reciprocals and Negative Exponents For any nonzero real numbers a and b and any integer n, n n a b b a (Any base to a power is equal to the reciprocal of the base raised to the opposite power.) Scientific Notation Scientific notation for a number is an expression of the type, N 10 m , where N is at least 1 but less than 10 (that is, 1 N 10 ), N is expressed in decimal notation, and m is an integer. Exercises: Express using positive exponents. Then, if possible, simplify. 1) 5) 2 4 3 1 2) 5 3 6) 3 4 3) (3) 4 7) x 2 11) y 5 y 2 4) xy 9 8) r v 12) x 4 5 Simplify. Do not use negative exponents in the answer. 9) 5 8 510 10) x 2 x 9 5 6 -1- Math 010 - Cooley Elementary Algebra OCC Section 4.8 – Negative Exponents and Scientific Notation Exercises: Simplify. Do not use negative exponents in the answer. 13) 4x 17) 5 x 8 y 3 z 2 5 y 6 3 16) 8a 6 2a 10 20) ( x 3 y 4 z 5 )( x 4 y 2 z 9 ) 9.043 10 3 24) 7.26 10 4 27) 370,000,000 28) 0.00000000952 30) 3 10 7 6 1012 14) x7 x 2 15) z 6 z 2 18) ( x 2 y 7 ) 5 19) 4a 3 b 2 5c 3 1.35 10 7 23) 0.0814 2 Convert to decimal notation. 21) 8.92 10 2 22) Convert to scientific notation. 25) 71,500 26) Multiply or divide, and write scientific notation. 29) (1.9 10 8 )(3.4 10 3 ) -2-