Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 8: Q. 8.70 (page 784)

Simplify:
a. $\frac{u^{\frac{4}{5}} 路 u^{\frac{- 2}{5}}}{u^{\frac{- 13}{5}}}$ b. ${(\frac{27 x^{\frac{4}{5}} y^{\frac{1}{6}}}{x^{\frac{1}{5}} y^{\frac{- 5}{6}}})}^{\frac{1}{3}}$

Short Answer

Expert verified

Part (a). The answer is $u^{3}$

Part (b). The answer is $3 x^{\frac{1}{5}} y$

Step by step solution

Part (a) Step 1. Simplifying the expression

Use the Product Property in the numerator, add the exponents.

$\frac{u^{\frac{4}{5}} 路 u^{\frac{- 2}{5}}}{u^{\frac{- 13}{5}}} \frac{u^{\frac{4}{5} - \frac{2}{5}}}{u^{\frac{- 13}{5}}} \frac{u^{\frac{2}{5}}}{u^{\frac{- 13}{5}}}$

Use the Quotient Property, subtract the

exponents,

$\frac{u^{\frac{2}{5}}}{u^{\frac{- 13}{5}}} u^{\frac{2}{5} - (\frac{- 13}{5})} u^{\frac{2 + 13}{5}} u^{\frac{15}{5}} u^{3}$

Part (b) Step 1. Simplifying the expression

Follow the order of operations to simplify inside the parentheses first.

Use the Quotient Property, subtract the

exponents.

${(\frac{27 x^{\frac{4}{5}} y^{\frac{1}{6}}}{x^{\frac{1}{5}} y^{\frac{- 5}{6}}})}^{\frac{1}{3}} {(\frac{27 x^{\frac{4}{5} - \frac{1}{5}}}{y^{\frac{- 5}{6} - \frac{1}{6}}})}^{\frac{1}{3}} {(\frac{27 x^{\frac{3}{5}}}{y^{- 1}})}^{\frac{1}{3}}$

Use the Product to a Power Property,

multiply the exponents.

${(\frac{27 x^{\frac{3}{5}}}{y^{- 1}})}^{\frac{1}{3}} \frac{27^{\frac{1}{3}} 路 x^{\frac{3}{5} 路 \frac{1}{3}}}{y^{- 1}} 3 x^{\frac{1}{5}} y$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Simplify:
a. $\frac{u^{\frac{4}{5}} 路 u^{\frac{- 2}{5}}}{u^{\frac{- 13}{5}}}$ b. ${(\frac{27 x^{\frac{4}{5}} y^{\frac{1}{6}}}{x^{\frac{1}{5}} y^{\frac{- 5}{6}}})}^{\frac{1}{3}}$

Short Answer

Step by step solution

Part (a) Step 1. Simplifying the expression

Part (b) Step 1. Simplifying the expression

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Applied Mathematics

Calculus

Geometry

Probability and Statistics

Logic and Functions

Study anywhere. Anytime. Across all devices.

91影视

Simplify:a.u45路u-25u-135b.27x45y16x15y-5613

Short Answer

Step by step solution

Part (a) Step 1. Simplifying the expression

Part (b) Step 1. Simplifying the expression

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Applied Mathematics

Calculus

Geometry

Probability and Statistics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Simplify:
a. $\frac{u^{\frac{4}{5}} 路 u^{\frac{- 2}{5}}}{u^{\frac{- 13}{5}}}$ b. ${(\frac{27 x^{\frac{4}{5}} y^{\frac{1}{6}}}{x^{\frac{1}{5}} y^{\frac{- 5}{6}}})}^{\frac{1}{3}}$