Beginning and Intermediate Algebra (6th Edition)
Beginning and Intermediate Algebra (6th Edition)
6th Edition
ISBN: 9780321969163
Author: Margaret L. Lial, John Hornsby, Terry McGinnis
Publisher: PEARSON
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Chapter A, Problem 1E
To determine

To calculate: The simplified form of the expression (a4b3)(a6b2).

Expert Solution & Answer
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Answer to Problem 1E

Solution:

The simplified expression of (a4b3)(a6b2) is 1a2b.

Explanation of Solution

Given Information:

The expression is (a4b3)(a6b2).

Formula used:

The definition of negative exponents states that for any nonzero real number a and integer n,

an=1an.

The Product rule states that for any real number a, and integers m and n,

aman=am+n.

Calculation:

Consider the expression.

(a4b3)(a6b2)

Apply the product rule to simplify the expression.

(a4b3)(a6b2)=(a4a6)(b3b2)=(a4+(6))(b(3)+2)

Add the exponents.

(a4b3)(a6b2)=(a2)(b1)=a2b1

Use the definition of the negative exponents to solve further.

(a4b3)(a6b2)=(1a2)(1b1)=1a2b

Therefore, the simplified expression of (a4b3)(a6b2) is 1a2b.

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