1. Review of Properties of Exponents

2. a 0 = 1, a  0 Properties of Exponents Assume throughout your work that no denominator is equal to zero and that m and n are positive integers. a -n = 1an1an a m  a n = a m+n amanaman = a m-n (ab) n = a n b n anbnanbn = abab n (a m ) n = a mn

3. Examples: (7a 2 )(-2a -5 ) = (7  -2)(a 2  a -5 ) = Group Coefficients and like variables. (-14)(a -3 ) = Apply properties. -14 a 3

4. Examples: (-2x -1 y 2 ) 3 = (-2) 3 (x -1 ) 3 (y 2 ) 3 = Share the outside power. (-8)(x -3 )(y 6 ) = Apply properties. -8y 6 x 3

5. Examples: Group Coefficients and like variables. (2)(a -2 )(b 4 )(c 0 ) = Apply properties. 2b 4 a 2 2ab 5 c 2 a 3 bc 2 = (2) = aa3aa3 b5bb5b c2c2c2c2

6. Simplify each expression. Use only positive exponents. (3a 2 )(4a 6 ) = (-4x 2 )(-2x -2 ) = (4x 3 y 5 ) 2 = (s 2 t) 3 (st) = (-6m 2 n 2 )(3mn)= 12a 8 8 16x 6 y 10 s7t4s7t4 -18m 3 n 3

7. Simplify each expression. Use only positive exponents. 4a 3 2x 8 y 5 8a 5 2a 2 = 6x 7 y 5 3x -1 = (4x 2 ) 0 2xy 5 = 1 2xy 5

8. Simplify each expression. Use only positive exponents. (2x -5 y 4 ) 3 = (3x 4 y 5 ) -3 = 8y 12 x 15 3x 2 2 = 2 9x 4 4 1 27x 12 y 15 (2r -1 s 2 t 0 ) -2 2rs = r 8s 5

9. Simplify each expression. Use only positive exponents. (p 2 ) -2 = (h 4 k 5 ) 0 = (3x -3 y -2 ) -2 = x 5 (2x) 3 = 1 8x 8 -5x 3 1p41p4 x6y49x6y49 -15x 4 3x =

10. Simplify each expression. Use only positive exponents. 2x 2 4x 3 2x = r 2 s 3 t 4 r 2 s 4 t -4 = (12x 2 y 6 ) 2 8x 4 y 7 = 18y 5 t8st8s