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Algebra 2
7.2    Properties of Rational Exponents

The same properties of exponents from 6.1 can be applied to rational exponents.

EX1: Simplify each expression.
                                                                         2
a)     51/2 ⋅ 51/ 4                        b)      (8
                                                       1/2
                                                             ⋅ 51/ 3 )




             4      −1/ 4                           7
c)     (2 ⋅ 3 )                            d)
         4
                                                   71/ 3




                    2
        121/ 3 
e)      41/ 3 
               


For a radical to be in simplest form, you must:
   • apply ______________________________ of exponents
   • remove any _________________________ nth powers
   • _____________________________ any denominators


EX2: Write the expression in simplest form.
                                                       3
a)     3
           54                              b)      5
                                                       4




                    1/2                             6xy1/2
c)     ( 9u v )
           2 10
                                           d)
                                                   2x1/ 3 z −5
Two radicals are _______________ ________________________ if and only if they
have the same:
   • _____________________________
   • _____________________________

EX3:
a)     5 y+6 ψ                               b)     3 3 5x 5 − ξ 3 40 ξ2




The weight in tons of a whale as a function of length in feet can be approximated by
                                     W = 0.1077 Λ3/2 .
Approximate the weight of a humpback whale with length 49.17 feet.




                     1                                                    1
A pilot whale is about  the length of a humpback whale. Is its weight also the
                     5                                                    5
weight of the humpback whale? If not, what is its weight?




HW p. 411 (30 – 38, 46 – 54, 62 – 72 even)

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A27 2 simplifyrads notes

  • 1. Algebra 2 7.2 Properties of Rational Exponents The same properties of exponents from 6.1 can be applied to rational exponents. EX1: Simplify each expression. 2 a) 51/2 ⋅ 51/ 4 b) (8 1/2 ⋅ 51/ 3 ) 4 −1/ 4 7 c) (2 ⋅ 3 ) d) 4 71/ 3 2  121/ 3  e)  41/ 3    For a radical to be in simplest form, you must: • apply ______________________________ of exponents • remove any _________________________ nth powers • _____________________________ any denominators EX2: Write the expression in simplest form. 3 a) 3 54 b) 5 4 1/2 6xy1/2 c) ( 9u v ) 2 10 d) 2x1/ 3 z −5
  • 2. Two radicals are _______________ ________________________ if and only if they have the same: • _____________________________ • _____________________________ EX3: a) 5 y+6 ψ b) 3 3 5x 5 − ξ 3 40 ξ2 The weight in tons of a whale as a function of length in feet can be approximated by W = 0.1077 Λ3/2 . Approximate the weight of a humpback whale with length 49.17 feet. 1 1 A pilot whale is about the length of a humpback whale. Is its weight also the 5 5 weight of the humpback whale? If not, what is its weight? HW p. 411 (30 – 38, 46 – 54, 62 – 72 even)