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Study Guide Algebra I Zero, Negative Exponents and Multiplying Powers Chapter 8, sections 1, 3 & 4, pages 430-451 Know the exponent rules and be able to use them. a m • a n = a m+n (ab) n = a n b n (a n ) m = a nm a0 = 1 1 a−n = n a € 1. Be able to simplify expressions or numbers raised to the zero power REMEMBER: anything to the zero power is 1 150 = 1 -(8x)0 = -1 (8x)0 = 1 but the – sign is not raised to the 0 power 4 0 − = 1 3 € 2. Be able to simplify expressions or numbers to the negative power REMEMBER: a negative exponent on the top goes to the bottom and becomes positive and a negative exponent on the bottom goes to the top and becomes positive. Examples: 1.) € m 2 n −3 the m2 stays on the top because it’s exponent is + the n-3 goes to the bottom because it’s exponent is – m 2 n −3 = 1 1 2.) € 3−2 = 2 = 3€ 9 € 3.) 9−1 m2 NOTE: the negative goes away when you move it. n3 move the 32 to the bottom flip the fraction because they are both negative exponents 3−2 9−1 −2 3 32 9 = 1 = =1 9 9 € 4.) € 7s0 t −5 −1 2 m the 7 & s0 stay on the top (positive exponents) and the m2 2 stays on the bottom (positive exponents) −5 the t goes to the bottom and the 2−1 and goes to the top (negative exponents) € 7s0 t −5 7 •1• 2 14 = 2 5 = 2 5 −1 2€ 2 m m t m t € REMEMBER: s0 = 1 € 3. Be able to simplify power to power expressions using the exponent rules Simplify the following expressions: 1.) (−2m−5n)−2 1 € (−2m−5n) 2 1 2 (−2) m € m10 4n 2 € 2.) € € −10 2 (5a 3b 2 ) 3 n negative exponent (-2) moves the entire expression to the denominator multiply exponents square (-2) & move the m −10 to the top 5 3 a 3•3b 2•3 75a 9b 6 € € 3.) € € € € € € distribute the exponent 3 to each element (2a−2b 3 ) 2 (ab 2 ) 3 2 2 a−2•2b 3•2 a1•3b 2•3 4a−4 b 6 a 3b 6 4a−4 a 3b 6b 6 4a−1b12 4b12 a € distribute the exponents 2 & 3 multiply the exponents rearrange terms add your exponents move a−1 to the denominator