Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
6.4 Rational Exponents Rational Exponent: Another way to write a radical expression. Like the radical form, the exponent form always indicates the principal root. The word exponent comes from the Latin word meaning “place outside.” Examples: √25 = 251/2 ³√27 = 271/3 4√16 = 161/4 Example 1: Simplifying Expressions with Rational Exponents 1a) 1251/3 Step 1: Rewrite as a Radical ³√125 Step 2: Simplify =5 1/2 1/2 1b) 5 (5 ) = √5 * √5 =5 1c) 101/3 (1001/3) = 1d) 161/4 1e) 21/2 (81/2) A rational exponent may have a numerator other than 1. The property (am)n = amn shows how to rewrite an expression with an exponent that is an improper fraction. There are two ways to rewrite the expression. Example: 1st) 253/2 = 25(³ * ½) = (25³)1/2 = √25³ or 2nd) 253/2= 25(½ * ³) = (251/2)³ = (√25)³ Property of Rational Exponents: If the nth root of a is a real number and m is an integer, then a1/n = n√a and am/n = n√am = n(√a)m. If m is negative, a ≠ 0. Example 2: Converting to and From Radical Form 2: Write the exponential expressions in radical form. 2a) x3/5 2b) y-2.5 2c) y-3/8 2: Write the radical expressions in exponential form. 2e) √a³ 2f) (5√b)² 2g) ³√x² 2h) (√y)³ 2d) z.4 Example 3: Simplifying Numbers with Rational Exponents You can simplify a number with a rational exponent by using the properties of exponents or by converting the expression to a radical expression. 3a) (-32) 3/5 3b) 4-3.5 3c)(-32) 4/5 Example 4: Writing Expressions in Simplest Form To write an expression with rational exponents in simplest form, write every exponent as a positive number. 4a) (16y-8)-3/4 4b) (8x-15) -1/3