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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. 5.36 (page 510)

Simplify each expression:
$鈸� {(z^{6})}^{9} 鈸� {(3^{7})}^{7} 鈸� {(q^{4})}^{5} {(q^{3})}^{3}$

Short Answer

Expert verified

The simplified expression of ${(z^{6})}^{9} = z^{54}$

The simplified expression of ${(3^{7})}^{7} = 3^{49}$

The simplified expression of ${(q^{4})}^{5} {(q^{3})}^{3} = q^{29}$

Step by step solution

01

Step 1. Given Information

In the given question we have to simplify each expression:

$鈸� {(z^{6})}^{9} 鈸� {(3^{7})}^{7} 鈸� {(q^{4})}^{5} {(q^{3})}^{3}$

02

Part (a) Step 1. The given expression is (z6)9

Use the Power Property, ${(a^{m})}^{n} = a^{m 路 n}$

${(z^{6})}^{9} = z^{6 路 9}$

Simplifying

${(z^{6})}^{9} = z^{54}$

03

Part (b) Step 1. The given expression is (37)7

Use the Power Property, ${(a^{m})}^{n} = a^{m 路 n}$

${(3^{7})}^{7} = 3^{7 路 7}$

Simplifying

role="math" localid="1644766001119" ${(3^{7})}^{7} = 3^{49}$

04

Part (c) Step 1. The given expression is (q4)5 (q3)3

Use the Power Property, ${(a^{m})}^{n} = a^{m 路 n}$

${(q^{4})}^{5} {(q^{3})}^{3} = (q^{4 路 5}) (q^{3 路 3})$

Simplifying

${(q^{4})}^{5} {(q^{3})}^{3} = (q^{20}) (q^{9})$

${(q^{4})}^{5} {(q^{3})}^{3} = q^{20 + 9} {(q^{4})}^{5} {(q^{3})}^{3} = q^{29}$

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