7.2 Properties of Rational Exponents OBJ: use properties of rational exponents & radicals and write expressions in simplest form Do Now: Simplify a)(-5) 4 · (-5) 5 b) (2xy 3 ) 4 c) (8) -2 d) e) (7b -3 ) 2 b 5 b

a m · a n =a m+n Product Property a m · a n =a m+n (a m ) n =a mn Power of a Power Property (a m ) n =a mn (ab) m =a m b m Power of a Product Property (ab) m =a m b m a -m = a≠0 Negative Exponent Property a -m = a≠0 a 0 =1 a≠0 Zero Exponent Property a 0 =1 a≠0 a m = a m-n a≠0 a n Quotient of Powers a m = a m-n a≠0 a n b≠0 Power of Quotient b≠0 Review Of Properties of Exponents Do Not Copy

(4 3 · 2 3 ) -1/3 c) (4 3 · 2 3 ) -1/3 (4 3 ) -1/3 · (2 3 ) -1/3 (4 3 ) -1/3 · (2 3 ) -1/ · · 2 -1 ¼ · ½ ¼ · ½ 1 / 8 1 / 8 d) *** The SAME properties that apply to integer exponents apply to rational exponents (no decimal answers) 6 1/2 · 6 1/3 a) 6 1/2 · 6 1/3 6 1/2 + 1/3 6 1/2 + 1/3 * on calculator: (1/2)+(1/3) enter MATH Frac 6 5/6 6 5/6 (27 1/3 · 6 1/4 ) 2 b) (27 1/3 · 6 1/4 ) 2 (27 1/3 ) 2 · (6 1/4 ) 2 (27 1/3 ) 2 · (6 1/4 ) /3 · 6 2/4 ( 3 √27) 2 · 6 1/2 ( 3 √27) 2 · 6 1/2 3 2 · 6 1/2 3 2 · 6 1/2 9 · 6 1/2 9 · 6 1/2 Ex 1:

Review of Properties of Radicals Product Property Quotient Property Do Not Copy

Write the expression in simplest form. = = a) = = = b) = = = = = = *** If the problem is in radical form to begin with, the answer should be in radical form as well a)b) 5 2 Ex 2: Ex 3: No tents in the basement!

Ex4: Perform the indicated operation 5(4 3/4 ) – 3(4 3/4 ) a) 5(4 3/4 ) – 3(4 3/4 ) 2(4 3/4 ) 2(4 3/4 )b) c) If the original problem is in radical form, the answer should be in radical form as well. If the problem is in rational exponent form, the answer should be in rational exponent form. *** Combine “like terms” HW

Day 2: Practice

continued… OBJ: use properties of rational exponents & radicals and write variable expressions in simplest form Do Now: Simplify 1)2)3)4)

Ex 1: Simplify the Expression a) b) (16g 4 h 2 ) 1/2 = 4g 2 h = 4g 2 hc) d)

Ex 2: Write the expression in simplest form. a) b) No tents in the basement! c) ** Remember, solutions must be in the same form as the original problem (radical form or rational exponent form)!!

d) No tents in the basement

Ex 3: Perform the indicated operation. a) b) c) d)

e) HW: