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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 5: Q. 143. (page 522)

In the following exercises, simplify each expression.
${(- 2 a^{3} b^{2})}^{4}$

Short Answer

Expert verified

The simplified form of the given expression is $16 a^{12} b^{8}$

Step by step solution

01

Step 1. Given information.

The given expression is ${(- 2 a^{3} b^{2})}^{4}$ .

02

Step 2. Simplify the given expression.

Calculation of expression using product property,

${(- 2 a^{3} b^{2})}^{4} = {(- 2)}^{4} 路 {(a^{3})}^{4} 路 {(b^{2})}^{4} = 16 路 {(a^{3})}^{4} 路 {(b^{2})}^{4}$

Now we use the power property

$16 路 {(a^{3})}^{4} 路 {(b^{2})}^{4} = 16 路 a^{3.4} 路 b^{2.4} = 16 a^{12} b^{8}$

Therefore, the simplified form of the given expression is $16 a^{12} b^{8}$

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