Q. 128 In the following exercises, simp... [FREE SOLUTION]

91影视

Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 6: Q. 128 (page 711)

In the following exercises, simplify each expression.
$鈸� {(5 a)}^{2} {(2 a)}^{3} 鈸� {(\frac{1}{2} y^{2})}^{3} {(\frac{2}{3} y)}^{2}$

Short Answer

Expert verified

(a) The simplified form of the given expression is $200 a^{5}$ .

(b) The simplified form of the given expression is $\frac{4}{72} y^{8}$ .

Step by step solution

Step 1. Given Information

In the following exercises, we have to simplify given expression.
$鈸� {(5 a)}^{2} {(2 a)}^{3} 鈸� {(\frac{1}{2} y^{2})}^{3} {(\frac{2}{3} y)}^{2}$

Part (a) Step 1. Given expression is (5a)2(2a)3

Use the Power Property.

${(5 a)}^{2} {(2 a)}^{3} = {{(5)}^{2} 路 (a)}^{2} {路 {(2)}^{3} 路 (a)}^{3} {(5 a)}^{2} {(2 a)}^{3} = {25 路 a}^{2} {路 8 路 a}^{3}$

Add the exponents.

${(5 a)}^{2} {(2 a)}^{3} = 25 路 {8 路 a}^{3 + 2} {(5 a)}^{2} {(2 a)}^{3} = 200 a^{5}$

Part (b) Step 1. Given expression is 12y23 23y2

Use the Power Property.

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

Add the exponents.

${(\frac{1}{2} y^{2})}^{3} {(\frac{2}{3} y)}^{2} = \frac{1}{8} 路 \frac{4}{9} 路 y^{2 + 6} {(\frac{1}{2} y^{2})}^{3} {(\frac{2}{3} y)}^{2} = \frac{4}{72} y^{8}$

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91影视

In the following exercises, simplify each expression.
$鈸� {(5 a)}^{2} {(2 a)}^{3} 鈸� {(\frac{1}{2} y^{2})}^{3} {(\frac{2}{3} y)}^{2}$

Short Answer

Step by step solution

Step 1. Given Information

Part (a) Step 1. Given expression is (5a)2(2a)3

Part (b) Step 1. Given expression is 12y23 23y2

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91影视

In the following exercises, simplify each expression.鈸�(5a)2(2a)3鈸�12y2323y2

Short Answer

Step by step solution

Step 1. Given Information

Part (a) Step 1. Given expression is (5a)2(2a)3

Part (b) Step 1. Given expression is 12y23 23y2

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Calculus

Applied Mathematics

Theoretical and Mathematical Physics

Statistics

Decision Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, simplify each expression.
$鈸� {(5 a)}^{2} {(2 a)}^{3} 鈸� {(\frac{1}{2} y^{2})}^{3} {(\frac{2}{3} y)}^{2}$