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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. 83. (page 520)

In the following exercises, simplify each expression using the properties for exponents.
$鈸� n^{19} 路 n^{12} 鈸� 3^{x} 路 3^{6} 鈸� 7 w^{5} 路 8 w 鈸� a^{4} 路 a^{3} 路 a^{9}$

Short Answer

Expert verified

The simplified form of given expression $n^{19} 路 n^{12} = n^{31}$

The simplified form of given expression $3^{x} 路 3^{6} = 3^{x + 6}$

The simplified form of given expression $7 w^{5} 路 8 w = 56 w^{6}$

The simplified form of given expression $a^{4} 路 a^{3} 路 a^{9} = a^{16}$

Step by step solution

01

Step 1. Given Information

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

$鈸� n^{19} 路 n^{12} 鈸� 3^{x} 路 3^{6} 鈸� 7 w^{5} 路 8 w 鈸� a^{4} 路 a^{3} 路 a^{9}$

02

Part (a) Step 1. The given expression is n19·n12

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

$n^{19} 路 n^{12} = n^{19 + 12}$

Simplify.

$n^{19} 路 n^{12} = n^{31}$

03

Part (b) Step 1. The given expression is 3x·36

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

$3^{x} 路 3^{6} = 3^{x + 6}$

04

Part (c) Step 1. The given expression is 7w5·8w

$7 w^{5} 路 8 w = 7 w^{5} 路 8 w^{1} 7 w^{5} 路 8 w = 7 路 8 路 w^{5} 路 w^{1}$

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

$7 w^{5} 路 8 w = 7 路 8 路 w^{5 + 1}$

Simplify.

$7 w^{5} 路 8 w = 56 w^{6}$

05

Part (d) Step 1. The given expression is a4·a3·a9

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

$a^{4} 路 a^{3} 路 a^{9} = a^{4 + 3 + 9}$

Simplify.

$a^{4} 路 a^{3} 路 a^{9} = a^{16}$

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