Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 5: Problem 2

Simplify \(\frac{8 r^{3}}{4 \pi r^{2}}\)

Short Answer

Expert verified
Question: Simplify the given expression: \(\frac{8 r^{3}}{4 \pi r^{2}}\) Answer: \(2r\)

Step by step solution

01

Identify the expression to be simplified

The given expression is \(\frac{8 r^{3}}{4 \pi r^{2}}\). Our task is to simplify this expression using the rules of fractions and exponents.
02

Simplify the fraction

First, let's simplify the fraction by dividing both numerator and denominator by their greatest common divisor, which is 4. This step gives \(\frac{8 r^{3}}{4 \pi r^{2}} = \frac{2 r^{3}}{\pi r^{2}}\).
03

Apply rules of exponents

Now, we will use the rules of exponents to further simplify the expression. According to the quotient rule, when dividing terms with the same base, we can subtract the exponents. Therefore, \(\frac{2 r^{3}}{\pi r^{2}}\) equals \(2 \cdot \frac{r^{3}}{r^{2}}\).
04

Simplify the expression

By applying the quotient rule for exponents, we get: \(2 \cdot r^{(3 - 2)} = 2r^{1}\).
05

Final answer

The simplified expression is: \(2r\), which is the final answer.

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!

One App. One Place for Learning.

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

Get started for free

Most popular questions from this chapter

Factorise (a) \(x^{2}+8 x-9\), (b) \(x^{2}+9 x-22\) (c) \(x^{2}+10 x+9\), (d) \(x^{2}+7 x+12\) (e) \(x^{2}-7 x+12\)

Factorise (a) \(14 x^{2}-127 x-57\) (b) \(45 x^{2}+44 x+7\), (c) \(6 x^{2}+19 x-11\).

(a) Express \(\frac{1}{u}+\frac{1}{v}\) as a single fraction. (b) Hence find the reciprocal of \(\frac{1}{u}+\frac{1}{v}\).

Remove the brackets from the given expression: \((2+x)(4+x)\)

Simplify (a) \(\frac{x}{4}+\frac{x}{5}\), (b) \(\frac{x}{4}+\frac{x}{5}+\frac{x}{6}\).
See all solutions

Recommended explanations on Physics Textbooks

Fields in Physics

Read Explanation

Solid State Physics

Read Explanation

Electricity

Read Explanation

Electric Charge Field and Potential

Read Explanation

Geometrical and Physical Optics

Read Explanation

Measurements

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free