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Intermediate Algebra – Student Workbook – Second Edition 2013

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Lesson 6b - Rational Exponents and Radical Functions<br />

Mini-Lesson<br />

THE NTH ROOT OF a<br />

n<br />

a = a 1 n , the nth root of a.<br />

On your TI 83/84 calculator, you can use the MATH>5: x sequence to compute nth roots.<br />

You can also use the ^ key to raise to fractional powers. You are recommended to put any<br />

fractional power in ( ).<br />

EXAMPLES:<br />

4<br />

a) 256 = 4<br />

b) <br />

2187 1 7<br />

3<br />

c) 15 1 3 2.<br />

47<br />

d) 6 324 is not a real number<br />

RATIONAL EXPONENTS<br />

EXAMPLES:<br />

( ) 3 4 4<br />

= 81<br />

a) 81<br />

( ) 3 = (3) 3 = 27<br />

2 3 3<br />

2<br />

b) ( 125) 125 ( 5)<br />

25<br />

c)<br />

2<br />

a p q =<br />

1 1 1 1<br />

32 2 5<br />

<br />

2 5<br />

2<br />

32<br />

2<br />

5<br />

32 2 4<br />

q<br />

a p<br />

q<br />

= ( a) p<br />

Problem 1<br />

MEDIA EXAMPLE <strong>–</strong> COMPUTE WITH RATIONAL/RADICAL<br />

EXPONENTS<br />

a) 49 <br />

3<br />

b) 8 <br />

49 d) 3 8 <br />

c) <br />

3 2<br />

e) 25<br />

f)<br />

3<br />

( 25)<br />

2<br />

Scottsdale Community College Page 266 <strong>Intermediate</strong> <strong>Algebra</strong>

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