6.2 Properties of Rational Exponents What you should learn: Goal1 Goal2 Use properties of rational exponents to evaluate and simplify expressions. Use properties of rational exponents to solve real-life problems. 6.2 Properties of Rational Exponents

Review of Properties of Exponents from section 6.1 a m * a n = a m+n (a m ) n = a mn (ab) m = a m b m a -m = = a m-n = These all work for fraction exponents as well as integer exponents.

Ex: Simplify. (no decimal answers) a.6 1/2 * 6 1/3 = 6 1/2 + 1/3 = 6 3/6 + 2/6 = 6 5/6 b. (27 1/3 * 6 1/4 ) 2 = (27 1/3 ) 2 * (6 1/4 ) 2 = (3) 2 * 6 2/4 = 9 * 6 1/2 c.(4 3 * 2 3 ) -1/3 = (4 3 ) -1/3 * (2 3 ) -1/3 = 4 -1 * 2 -1 = ¼ * ½ = 1 / 8 d. = = = ** All of these examples were in rational exponent form to begin with, so the answers should be in the same form!

Ex: Simplify. a. = = = 5 b. = = = 2 Ex: Write the expression in simplest form. a. = = = b. = = = = Can’t have a Radical in the basement! ** If the problem is in radical form to begin with, the answer should be in radical form as well.

Ex: Perform the indicated operation a.5(4 3/4 ) – 3(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.

More Examples a. b. c. d.

Ex: Simplify the Expression. Assume all variables are positive. a. b.(16g 4 h 2 ) 1/2 = 16 1/2 g 4/2 h 2/2 = 4g 2 h c. d.

Reflection on the Section Can you find the quotient of two radicals with different indices? Assignment Pg. 6.2 Properties of Rational Exponents Yes, Change both to rational exponent form and use the quotient property.