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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 9: Q578. (page 1144)

Simplify: $a) {(9 p^{\frac{2}{3}})}^{\frac{5}{2}} b) {(27 q^{\frac{3}{2}})}^{\frac{4}{3}} .$

Short Answer

Expert verified

$P a r t a) {(9 p^{\frac{2}{3}})}^{\frac{5}{2}} = 243 p^{\frac{5}{3}} P a r t b) {(27 q^{\frac{3}{2}})}^{\frac{4}{3}} = 81 q^{2} .$

Step by step solution

01

Part (a) Step 1 : Given Information

The given expression is ${(9 p^{\frac{2}{3}})}^{\frac{5}{2}} .$

02

Part (a) Step 2: Simplification

${(9 p^{\frac{2}{3}})}^{\frac{5}{2}} = {(3)}^{2 脳 \frac{5}{2}} 脳 {(p)}^{\frac{2}{3} 脳 \frac{5}{2}} = 3^{5} 脳 p^{\frac{5}{3}} = 243 p^{\frac{5}{3}} H e n c e, {(9 p^{\frac{2}{3}})}^{\frac{5}{2}} = 243 p^{\frac{5}{3}} .$

03

Part (b) Step 1: Given information

The given expression is ${(27 q^{\frac{3}{2}})}^{\frac{4}{3}} .$

04

Part (b) Step 2: Simplification

${(27 q^{\frac{3}{2}})}^{\frac{4}{3}} = {(3)}^{3 脳 \frac{4}{3}} 脳 q^{\frac{3}{2} 脳 \frac{4}{3}} = 3^{4} 脳 q^{2} = 81 q^{2} H e n c e, {(27 q^{\frac{3}{2}})}^{\frac{4}{3}} = 81 q^{2} .$

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