Chapter P.4, Problem 66E

### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

Chapter
Section

### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem
1 views

# 59-68 Simplifying Expressions Involving Rational ExponentsSimplify the expression and eliminate any negative exponent(s). Assume that all letters denote positive numbers. ( a ) ( x − 5 y 1 / 3 ) − 3 / 5                         ( b ) ( 4 r 8 t − 1 / 2 ) 1 / 2 ( 32 t − 5 / 4 ) − 1 / 5

To determine

a)

To simplify:

The given expression (x5y1/3)3/5.

Explanation

Definition for Rational Exponents:

am/n=(an)m=amn

The exponent m/n consists of two parts:

The denominator n is the root and the numerator m is the exponent.

aâˆ’m/n=1am/n

Exponent Rules:

abâ‹…ac=ab+c

xaxb=xbâˆ’a(ab)c=abc

Calculation:

Given:

(xâˆ’5y1/3)âˆ’3/5

Apply exponent rule: aâˆ’m/n=1am/n

(xâˆ’5y1/3)âˆ’3/5=1(xâˆ’5y1/3)3/5=1(y1/3x5)3/5(xâˆ’5y1/3)âˆ’3/5=1(y1/3x5)3/5...................(1)

Apply exponent rule:(aâ‹…b)n=anbn

To determine

b)

To simplify:

The given expression (4r8t1/2)1/2(32t5/4)1/5

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