University:
High School
Course:
High School Mathematics
Academic year:

2022
Views:

312

Pages:

10
Author:

Yasmine Burch

nth Roots and Rational Exponents For use with Exploration 5.1 Essential Question How can you use a rational exponent to represent a power involving a radical? EXPLORATION: Writing Expressions in Rational Exponent Form Go to BigldeasMath.com for an interactive tool to investigate this exploration. Work with a p�rtner. Use the definition of a rational e�R'?�ent and the properties of exponents to • nte e�ch e:�res �9. _as a_Q. a_§e �i� �. in_g!e cati pal e:x,29�� Then tIB.::!!iil?ui¥ t�ch _ expresston. Roued yom answerfo two dee1mnl plaees. r::- Sample � 2'.52 IT 27 3l I . ( )� 1 . ;,1·'5 "1.) 123 nth Roots and Rational Exponents (continued) EXPLORATION: Writing Expressions in Radical Form Go to BigldeasMath.com for an interactive tool to investigate this exploration. Work with a partner. Use the properties of exponents and the definition of a rational exponent to write each expression as a radical raised to an exponent. Sample 5 2/3 g2/3 a. = (s l/3 2 ) l- = �( J1r) (- (�\ -: 7 '/' �@ c. 1 i3!.4 ti J1 �-·--·�--• . �;·,·°? 2- - ;bJ%") � d. 103/2 ;.. JGS' f. 206/5 Or'_,-' '2....0 b ,_ i ;. F u•'lA-'•'1 O•? o,2-0 � CJZD )�OW') wallc.-. Notetaking with Vocabulary •• -� �·te.. For use after Lesson 5.1 Core Concepts � i ·:i,e.. ', Let n be an integer (n > 1) and let a be a real number. {2-) I,,{ J I 0) I&".,) n is a$integer. 'No� ��r ,-- n is a � efo Jo ) a = 0 J�);:: �3, Rational Exponents Let al/n be an nth root of a, and let m be a positive integer. amfn' = (Jl/n)m � "� u 1 a-m/n - a mfn \ = (*)m 0( 1 -a -:t-0 1 -=-=-m' (a f n ) l m ) ¼ ( = n a l/ (r Z--/q :: JB : ;, l); ( I > '$, ;-_/'l) � One real nth root: a = 0 -b;. t, e.. ,, red i/1. Real :hth roots of a ' t f o ..�. i) One real nth root: efo �- 1