Chapter 8: Q. 8.65 (page 782)

Simplify:
a. $x^{\frac{1}{6}} \cdot x^{\frac{4}{3}}$ b. ${(x^{6})}^{\frac{4}{3}}$ c. $\frac{x^{\frac{2}{3}}}{x^{\frac{5}{3}}}$

Short Answer

Expert verified

Part (a). The answer is $x^{\frac{3}{2}}$ .

Part (b). The answer is $x^{8}$ .

Part (c). The answer is $\frac{1}{x}$ .

Step by step solution

Part (a) Step 1. Simplifying

We know that if the base of the exponent is the same in the multiplication then we have to add the powers.

So,

$= x^{\frac{1}{6}} \cdot x^{\frac{4}{3}} = x^{\frac{1}{6} + \frac{4}{3}} = x^{\frac{1 + 8}{6}} = x^{\frac{9}{6}} = x^{\frac{3}{2}}$

Part (b) Step 1. Simplifying the exponent

We know that,

${(a^{b})}^{c} = a^{b \cdot c}$

Similarly,

$= {(x^{6})}^{\frac{4}{3}} = x^{6 \cdot \frac{4}{3}} = x^{2 \cdot 4} = x^{8}$

Part (c) Step 1. Simplifying the exponent

We know that, $\frac{a^{b}}{a^{c}} = a^{b - c}$

Similarly,

localid="1644693096053" $= \frac{x^{\frac{2}{3}}}{x^{\frac{5}{3}}} = x^{\frac{2}{3} - \frac{5}{3}} = x^{\frac{2 - 5}{3}} = x^{\frac{- 3}{3}} = x^{- 1} = \frac{1}{x}$

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Simplify:
a. $x^{\frac{1}{6}} \cdot x^{\frac{4}{3}}$ b. ${(x^{6})}^{\frac{4}{3}}$ c. $\frac{x^{\frac{2}{3}}}{x^{\frac{5}{3}}}$

Short Answer

Step by step solution

Part (a) Step 1. Simplifying

Part (b) Step 1. Simplifying the exponent

Part (c) Step 1. Simplifying the exponent

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Probability and Statistics

Logic and Functions

Mechanics Maths

Pure Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Simplify:a.x16·x43b.x643c.x23x53

Short Answer

Step by step solution

Part (a) Step 1. Simplifying

Part (b) Step 1. Simplifying the exponent

Part (c) Step 1. Simplifying the exponent

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Probability and Statistics

Logic and Functions

Mechanics Maths

Pure Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Simplify:
a. $x^{\frac{1}{6}} \cdot x^{\frac{4}{3}}$ b. ${(x^{6})}^{\frac{4}{3}}$ c. $\frac{x^{\frac{2}{3}}}{x^{\frac{5}{3}}}$