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8.1 Multiplication Properties of Exponents

8.1 Multiplication Properties of Exponents. Exponent Vocabulary. a n = a • a • a ….. a n times. Base number : the number being multiplied. a is the base number. Power : the number of times the base is multiplied. n is the power.

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8.1 Multiplication Properties of Exponents

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  1. 8.1 Multiplication Properties of Exponents

  2. Exponent Vocabulary an = a • a • a…..an times Base number: the number being multiplied. a is the base number. Power: the number of times the base is multiplied. n is the power.

  3. Rules for multiplying with exponents when you have the SAME BASE! PRODUCT OF POWERS PROPERTY Multiplication with the same base: am • an = am+nadd exponents

  4. POWER OF POWER PROPERTY Powers of powers with the same base: (am)n = amn multiply exponents

  5. Power of a Product Property Different bases, distribute power to each base and multiply. Examples: (a • b)4 = a4 • b4 = a4b4 (-3x)2 = (-3) 2• x 2 = 9x2

  6. Try these! • 65642.102109 69 = 10,077,696 1011 = 100,000,000,000 3. (2x)3 4. [(5x)3]6 (5x)18 = 5 18 x18 23x3 = 8x3

  7. Something fun to do with exponents… a>1 the equation is a model for exponential growth. a<1 the equation is a model for exponential decay.

  8. Example: ax Graph 2x 0.6x Growth Decay

  9. Some final exponent practice problems… 3y2(2y)3 (r2st3)2(s4t)3 3y223y3 = 3 23y5 =24y5 = r4s2t6s12t3 = r4s14t9

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