Mini-Lecture 8.7: Rational Exponents | Montgomery College - Edubirdie

University:
Montgomery College
Course:
MATH 130: Elements of Mathematics I: Mathematical Reasoning and Number Systems
Academic year:

2023
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359

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1
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Uszewskadndr

Mini-Lecture 8.7 Rational Exponents Learning Objectives: 1. Evaluate exponential expressions of the form a1/ n . 2. Evaluate exponential expressions of the form a m / n . 3. Evaluate exponential expressions of the form a −m / n . 4. Use rules for exponents to simplify expressions containing fractional exponents. Examples: 1. Evaluate exponential expressions of the form a1/ n Write in radical form and then simplify. a) 1 36 2 b) 1 1 13 ⎛ 1 ⎞3 c) ⎜ ⎟ ⎝ 1000 ⎠ 2. Evaluate exponential expressions of the form a m / n . Write first in radical form, then simplify. a) 3 92 2 b) 64 3 c) 3 −814 3. Evaluate exponential expressions of the form. a −m / n . Write first in radical form, then simplify. a) 4 − 1 2 b) 16 − 3 4 c) 125 − 2 3 4. Use rules for exponents to simplify expression containing fractional exponents. a) 4 27 3 1 ⋅ 27 3 b) 4 64 3 3 −25 2 5 64 3 Teaching Notes: • • • • Identify the power and the index of the exponent before students work the problem. Remind students a negative outside the parentheses is not affected by the exponent Review exponent rules before simplifying expressions. Each section in the text has 3 worksheets in the Extra Practice featuring differentiated learning. Answers: 1a) 3a) 1 1 1 , 3b) ; 3c) ; 4a) 8 25 2 ( 3 ( ) 3 1 1 ; 2a) 9 , 27; 2b) = 1000 10 5 3 1 1 27 ,35 ; 4b) 3 , ; 4c) − 25 , −53 64 4 36 = 6 ; 1b) 3 1 = 1 ; 1c) ) 3 ( ) ( 3 ) 2 64 , 16; 2c) − ( 81 ) , -27; 4 3

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