Laws of Exponents

Multiplication of Powers b (a+b) x x = x • x9 x3•x4•x2 = x3+4+2 = x3y6 x2y4•xy2= x2+1y4+2 = 3x3y•2xy2= 3•2 x3+1y1+2 = 6x4y3

Robert Duncan 2007 Alief Taylor Math Dept Division of Powers a x (a – b) = x x b 9x5 3x2 = 3x5-2 = 3x3 10x5y7z3 2x3y2z 5x2y5z2 = 5x5-3y7-2z3-1= Robert Duncan 2007 Alief Taylor Math Dept

Robert Duncan 2007 Alief Taylor Math Dept Powers of Powers b (xa) = xab (x4)5 = x4x5 = x20 (x3y4)2 = x3x2y4x2 = x6y8 [(x4)2]3 = x4x2x3 = x24 Robert Duncan 2007 Alief Taylor Math Dept

Robert Duncan 2007 Alief Taylor Math Dept Negative Exponents 1 x-a x-a = 1 xa and = xa 1 x5 x-5 = x2y-4 = x2 y4 Robert Duncan 2007 Alief Taylor Math Dept

Robert Duncan 2007 Alief Taylor Math Dept Zero Exponent x0 = 1 x4x-4 = x4+(-4) = x0 = 1 x3-3 = x0 = 1 x3 = Robert Duncan 2007 Alief Taylor Math Dept

x2y3 x4y8 1 x2y5 =x-2 y-5 = x2-4 y3-8

2x3y-3 2x-1y2 4x3+-1 y-3+2 =4x2y-1 4x2 y

6x4yz3 3x2y3z4 2x4-2 y1-3z3-4 =2x2 y-2z-1 2x2 y2z

Negative Exponent Rule 4x3y4 5x2y8 5x2y-6 2y2 Product Rule • Quotient Rule (4•5)x3+2y4+-6 20x5y-2 = = (5•2)x2y8+2 10x2y10 2x3 y12 2x5-2y-2-10 2x3y-12 = = Negative Exponent Rule