Chapter 6: Q. 129 (page 711)

In the following exercises, simplify each expression.
$ⓐ {(4 b)}^{2} {(3 b)}^{3} ⓑ {(\frac{1}{2} j^{2})}^{5} {(\frac{2}{5} j^{3})}^{2}$

Short Answer

Expert verified

(a) The simplified form of the given expression is $432 b^{5}$ .

(b) The simplified form of the given expression is $\frac{1}{200} j^{16}$ .

Step by step solution

Step 1. Given Information

In the following exercises, we have to simplify given expression.
$ⓐ {(4 b)}^{2} {(3 b)}^{3} ⓑ {(\frac{1}{2} j^{2})}^{5} {(\frac{2}{5} j^{3})}^{2}$

Part (a) Step 1. Given expression is (4b)2(3b)3

Use the Power Property.

${(4 b)}^{2} {(3 b)}^{3} = {{(4)}^{2} \cdot (b)}^{2} {\cdot {(3)}^{3} \cdot (b)}^{3} {(4 b)}^{2} {(3 b)}^{3} = {16 \cdot b}^{2} {\cdot 27 \cdot b}^{3}$

Add the exponents.

${(4 b)}^{2} {(3 b)}^{3} = 16 \cdot {27 \cdot b}^{3 + 2} {(4 b)}^{2} {(3 b)}^{3} = 432 b^{5}$

Part (b) Step 1. Given expression is 12j2525j32

Use the Power Property.

${(\frac{1}{2} j^{2})}^{5} {(\frac{2}{5} j^{3})}^{2} = {(\frac{1}{2})}^{5} \cdot {(j^{2})}^{5} \cdot {(\frac{2}{5})}^{2} \cdot {(j^{3})}^{2} {(\frac{1}{2} j^{2})}^{5} {(\frac{2}{5} j^{3})}^{2} = \frac{1}{32} \cdot j^{2 \cdot 5} \cdot \frac{4}{25} \cdot j^{3 \cdot 2} {(\frac{1}{2} j^{2})}^{5} {(\frac{2}{5} j^{3})}^{2} = \frac{1}{32} \cdot j^{10} \cdot \frac{4}{25} \cdot j^{6}$

Add the exponents.

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

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In the following exercises, simplify each expression.
$ⓐ {(4 b)}^{2} {(3 b)}^{3} ⓑ {(\frac{1}{2} j^{2})}^{5} {(\frac{2}{5} j^{3})}^{2}$

Short Answer

Step by step solution

Step 1. Given Information

Part (a) Step 1. Given expression is (4b)2(3b)3

Part (b) Step 1. Given expression is 12j2525j32

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In the following exercises, simplify each expression.ⓐ(4b)2(3b)3ⓑ12j2525j32

Short Answer

Step by step solution

Step 1. Given Information

Part (a) Step 1. Given expression is (4b)2(3b)3

Part (b) Step 1. Given expression is 12j2525j32

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Decision Maths

Mechanics Maths

Theoretical and Mathematical Physics

Geometry

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises, simplify each expression.
$ⓐ {(4 b)}^{2} {(3 b)}^{3} ⓑ {(\frac{1}{2} j^{2})}^{5} {(\frac{2}{5} j^{3})}^{2}$