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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 11: Q. 84. (page 1069)

In the following exercises, simplify each expression using the properties for exponents.
$鈸� q^{27} 路 q^{15} 鈸� 5^{x} 路 5^{4 x} 鈸� 9 u^{41} 路 7 u^{53} 鈸� c^{5} 路 c^{11} 路 c^{2}$

Short Answer

Expert verified

The simplified form of given expression $q^{27} 路 q^{15} = q^{42}$

The simplified form of given expression $5^{x} 路 5^{4 x} = 5^{5 x}$

The simplified form of given expression $9 u^{41} 路 7 u^{53} = 63 u^{94}$

The simplified form of given expression $c^{5} 路 c^{11} 路 c^{2} = c^{18}$

Step by step solution

01

Step 1. Given Information

In the given question we have to simplify the given expression:

$鈸� q^{27} 路 q^{15} 鈸� 5^{x} 路 5^{4 x} 鈸� 9 u^{41} 路 7 u^{53} 鈸� c^{5} 路 c^{11} 路 c^{2}$

02

Part (a) Step 1. The given expression is q27·q15

Use the Product Property, $a^{m} 路 a^{n} = a^{m + n}$

$q^{27} 路 q^{15} = q^{27 + 15}$

Simplify.

$q^{27} 路 q^{15} = q^{42}$

03

Part (b) Step 1. The given expression is 5x·54x

Use the Product Property, $a^{m} 路 a^{n} = a^{m + n}$

$5^{x} 路 5^{4 x} = 5^{x + 4 x}$

Simplify.

$5^{x} 路 5^{4 x} = 5^{5 x}$

04

Part (c) Step 1. The given expression is 9u41·7u53

$9 u^{41} 路 7 u^{53} = 9 路 7 路 u^{41} 路 u^{53}$

Use the Product Property, $a^{m} 路 a^{n} = a^{m + n}$

$9 u^{41} 路 7 u^{53} = 9 路 7 路 u^{41 + 53}$

Simplify.

$9 u^{41} 路 7 u^{53} = 63 u^{94}$

05

Part (d) Step 1. The given expression is c5·c11·c2

Use the Product Property, $a^{m} 路 a^{n} = a^{m + n}$

$c^{5} 路 c^{11} 路 c^{2} = c^{5 + 11 + 2}$

Simplify.

$c^{5} 路 c^{11} 路 c^{2} = c^{18}$

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