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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. 130. (page 521)

In the following exercises, simplify each expression by applying several properties.
$(a) . {(3 p q^{4})}^{2} {(6 p^{6} q)}^{2} (b) . \frac{{(- 2 k^{- 3})}^{2} {(6 k^{2})}^{4}}{{(9 k^{4})}^{2}}$

Short Answer

Expert verified

The simplified form of the expressions

$(a) . {(3 p q^{4})}^{2} {(6 p^{6} q)}^{2} = 324 p^{14} q^{10} (b) . \frac{{(- 2 k^{- 3})}^{2} {(6 k^{2})}^{4}}{{(9 k^{4})}^{2}} = \frac{64}{k^{6}}$

Step by step solution

01

Part (a) Step 1. Given information.

The given expression is ${(3 p q^{4})}^{2} {(6 p^{6} q)}^{2}$ .

02

Part (a) Step 2. Apply the product to a power property.

Apply the concept of product power-

${(3 p q 4)}^{2} {(6 p 6 q)}^{2} = 3^{2} . p^{2} . {(q^{4})}^{2} 脳 6^{2} . {(p^{6})}^{2} . q^{2} = 9 p^{2} q^{8} 36 p^{12} q^{2} = 324 p^{14} q^{10} .$

03

Part (b) Step 1. Given information.

The given expression is $\frac{{(- 2 k^{- 3})}^{2} {(6 k^{2})}^{4}}{{(9 k^{4})}^{2}}$ .

04

Part (b) Step 2. Apply the concept of power property.

Apply the power product rule-

$\frac{{(- 2 k^{- 3})}^{2} {(6 k^{2})}^{4}}{{(9 k^{4})}^{2}} = \frac{- 2^{2} {(k^{- 3})}^{2} . 6^{4} . {(k^{2})}^{4}}{9^{2} . {(k^{4})}^{2}} = \frac{4 脳 1296 脳 k^{2}}{81 脳 k^{8}} = \frac{64}{k^{6}}$

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