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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 11: Q. 156 (page 1069)

Simplify
(a) ${(\frac{1}{2} y^{2})}^{3} {(\frac{2}{3} y)}^{2}$
(b) ${(\frac{1}{2} j^{2})}^{5} {(\frac{2}{5} j^{3})}^{2}$

Short Answer

Expert verified

Simplified expressions are

(a) $\frac{y^{8}}{18}$

(b) $\frac{j^{16}}{200}$

Step by step solution

01

part (a) Step 1 Given information

${(\frac{1}{2} y^{2})}^{3} {(\frac{2}{3} y)}^{2}$

02

part (a) Step 2

${(\frac{1}{2} y^{2})}^{3} {(\frac{2}{3} y)}^{2} = {(\frac{1}{2})}^{3} {(y^{2})}^{3} {(\frac{2}{3})}^{2} {(y)}^{2} = \frac{1}{2^{3}} 脳 y^{2 脳 3} 脳 \frac{2^{2}}{3^{2}} 脳 y^{2} = \frac{1}{8} 脳 y^{6} 脳 \frac{4}{9} 脳 y^{2} = \frac{1}{18} 脳 y^{6 + 2} = \frac{y^{8}}{18}$

03

part (b) Step 1 Given information

${(\frac{1}{2} j^{2})}^{5} {(\frac{2}{5} j^{3})}^{2}$

04

part (b) Step 2

${(\frac{1}{2} j^{2})}^{5} {(\frac{2}{5} j^{3})}^{2} = {(\frac{1}{2})}^{5} {(j^{2})}^{5} {(\frac{2}{5})}^{2} {(j^{3})}^{2} = \frac{1}{2^{5}} 脳 j^{2 脳 5} 脳 \frac{2^{2}}{5^{2}} 脳 j^{3 脳 2} = \frac{1}{32} 脳 j^{10} 脳 \frac{4}{25} 脳 j^{6} = \frac{1}{200} 脳 j^{10 + 6} = \frac{j^{16}}{200}$

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