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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 8: Q 79. (page 930)

In the following exercises, multiply.
$\frac{12 a^{3} b}{b^{2}} 路 \frac{2 a b^{2}}{9 b^{3}}$

Short Answer

Expert verified

The required answer is $\frac{8 a^{4}}{3 b^{2}}$ .

Step by step solution

01

Step 1. Given information.

The given expression is:

$\frac{12 a^{3} b}{b^{2}} 路 \frac{2 a b^{2}}{9 b^{3}}$

02

Step 2. Simplify the expression.

$\frac{12 a^{3} b}{b^{2}} 路 \frac{2 a b^{2}}{9 b^{3}}$

Multiply the numerators and denominators,

$\frac{12 a^{3} b 路 2 a b^{2}}{b^{2} 路 9 b^{3}}$

Factor the numerator and denominator completely, and then remove common factors,

$\frac{3 路 4 路 a 路 a 路 a 路 b 路 2 路 a 路 b 路 b}{b 路 b 路 3 路 3 路 b 路 b 路 b}$

Simplify,

$\frac{8 a^{4}}{3 b^{2}}$

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