Laws of Exponents

Laws of Exponents Whenever we have variables which contain exponents and have equal bases, we can do certain mathematical operations to them. Those operations are called the “Laws of Exponents” x b b = base x = exponent Free powerpoints at http://www.worldofteaching.com Laws of Exponents 1. x  x  x m n m n 2.  xy   x y m m m 3. x   m n x mn x x 4.    m  y y   m m m x mn 5a. if m  n , then n  x x m x 1 5b. if n  m , then n  n  m x x Other Properties of Exponents x 1 0 Any single number or variable is always to the first power 1 x  x 1 33 1 aa 1 2 x  2 x  2 x  1 1 1 Basic Examples x x  x 2 3 23 x 12 5 x  4 3 x 43 x 3  xy  3 x y 3 Basic Examples x x    3  y y   7 74 x x 3   x 4 x 1 5 x 1 1  7 5  2 7 x x x 3 3 More Examples 2m n  3  5r 2  8r 3  2r 2   5  8  2r 23 2   80r 7 2 5 3 2a 3  7a 4  2  7 a 34  14a 7 2 m n 13 23 53  2 m n  8m n 3 6 15 6 15 33 x 3 y 3  27 x 3 y 3 3xy    2a     3b  4 8x  2x 9z3  5 3z 2 2 2 a 2 4a 2  2 2  2 3 b 9b 4 1 8x  4x 3 2 1 1 9 1 3 3 2  2 5 3 x 3z x More Examples 3x 3 y 2 z  7 xyz 2  3  7 x 31 y 21 z1 2  21 x 4 y 3 z 3  8 xy 2  3xy   2 xy 3   8  3  2x111 y 213  48 x 3 y 6   3x y  2xy 2 3 2 2 2   3 12 x 22 y 32 212 x12 y 22    9 x 4 y 6  4 x 2 y 4  9  4 x 4 2 y 6 4  36 x 6 y10 3  5a b  513 a 33b13 53 a 9b 3 125 a 9b 3 125 a 9 3 125 a 6   3ab 2   313 a13b 23  33 a 3b 6  27 a 3b 6  27 b 6 3  27 b 3    3