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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. 31 (page 1069)

Multiply the rational expressions $\frac{5 x^{2} y^{4}}{12 x y^{3}} 脳 \frac{6 x^{2}}{20 y^{2}}$

Short Answer

Expert verified

The simplified form of form of rational expressions $\frac{5 x^{2} y^{4}}{12 x y^{3}} 脳 \frac{6 x^{2}}{20 y^{2}} i s \frac{x^{3}}{8 y} .$

Step by step solution

01

. Given information

Given expressions are $\frac{5 x^{2} y^{4}}{12 x y^{3}} a n d \frac{6 x^{2}}{20 y^{2}}$ .

We have to multiply these expressions.

02

. Multiplication of rational expressions

To simplify first multiply numerators and denominators and then simplify by dividing out the common factors. Hence multiplied form of given rational expressions is $\frac{5 x^{2} y^{4}}{12 x y^{3}} 脳 \frac{6 x^{2}}{20 y^{2}} = \frac{5 x^{2} y^{4} 脳 6 x^{2}}{12 x y^{3} 脳 20 y^{2}} = \frac{5 脳 6 x^{4} y^{4}}{12 脳 20 x y^{5}}, \sin c e a^{m} 脳 a^{n} = a^{m + n} = \frac{x^{3}}{8 y}, d i v i d e o u t t h e c o m m o n f a c t o r s$

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Most popular questions from this chapter

Use the Quotient Property to simplify square roots.

$\sqrt{\frac{180 s^{10}}{144}}$

In the following exercises, convert each number to decimal form.

(a) $- 8.3 脳 10^{2}$ (b) $3.8 脳 10^{- 2}$

Use the Quotient Property to Simplify Radical Expressions

In the following exercises, use the Quotient Property to simplify square roots.

$a . \sqrt{\frac{72}{98}} b . \sqrt[3]{\frac{24}{81}} c . \sqrt[4]{\frac{6}{96}}$

Show two different algebraic methods to simplify $4^{\frac{3}{2}}$ . Explain all your steps.

Simplify the rational expression $\frac{3 m^{2} + 30 m n + 75 n^{2}}{4 m^{2} - 100 n^{2}}$

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