5.2 Properties of Rational Exponents

Learning Objectives I will be able to… Write Expressions in Radical Form Write Expressions in Rational Exponential Form Simplify and Solve Rational Exponent Expressions

Review of Properties of Exponents from section 6.1 am · an = am+n (am)n = amn (ab)m = ambm a0 =1 a-m = = am-n = These all work for fraction exponents as well as integer exponents.

Ex: Simplify. (no decimal answers) (43 · 23)-1/3 = (43)-1/3 · (23)-1/3 = 4-1 · 2-1 = ¼ · ½ = 1/8 d. = = = 61/2 · 61/3 = 61/2 + 1/3 = 63/6 + 2/6 = 65/6 b. (271/3 · 61/4)2 = (271/3)2 · (61/4)2 = (3)2 · 62/4 = 9 · 61/2 ** All of these examples were in rational exponent form to begin with, so the answers should be in the same form!

Laws of Rational Exponents   RULES No Negative Exponents No Rational Exponents

Ex: Write the expression in simplest form. Ex: Simplify. = = = 5 = = 2 Ex: Write the expression in simplest form. = = = Can’t have a tent 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 5(43/4) – 3(43/4) = 2(43/4) 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. b. (16g4h2)1/2 = 161/2g4/2h2/2 = 4g2h c. d.

Ex: Write the expression in simplest form Ex: Write the expression in simplest form. Assume all variables are positive. 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. Can’t have a tent in the basement!!

Ex: Perform the indicated operation. Assume all variables are positive.

e.

Solve  

Homework Textbook pg. 178 #7-14, 29-34