Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 5: Problem 9

Remove the brackets from \(\left(7 x^{2}\right)^{-3} .\)

Short Answer

Expert verified
Question: Remove the brackets from the expression \(\left(7 x^{2}\right)^{-3}\) and simplify. Answer: \(\frac{1}{343}x^{-6}\)

Step by step solution

01

Distribute the exponent

Distribute the exponent \(-3\) to both the coefficient \(7\) and the variable \(x^{2}\) inside the brackets. \((7x^{2})^{-3} \Rightarrow 7^{-3}(x^{2})^{-3}.\)
02

Apply exponent rules for the variable

Apply the exponent rules for the variable \(x^{2}\). Remember that when taking the power of a power, we multiply the exponents. So, \((x^{2})^{-3} \Rightarrow x^{(2 \times -3)} \Rightarrow x^{-6}\).
03

Simplify the coefficient

Now, simplify the coefficient \(7^{-3}\) which means \(\frac{1}{7^3}\) or \(\frac{1}{343}\).
04

Write the final result

Combine the simplified coefficient and variable to obtain the final simplified expression. The simplified expression is \(\frac{1}{343}x^{-6}\).

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

Simplify \(\frac{x+2}{x^{2}+9 x+20} \times \frac{x+5}{x+2}\).

Factorise (a) \(2 x^{2}-11 x+5\) (b) \(2 x^{2}+13 x+15\)

Remove the square brackets from $$ \frac{1}{\omega}\left[\frac{s \omega}{s^{2}+\omega^{2}}-s\right] $$

Remove the brackets from the given expression: \((x-1)(x+2)\)

Remove the brackets from the given expression: \(7(2 x+y)\)
See all solutions

Recommended explanations on Physics Textbooks

Turning Points in Physics

Read Explanation

Modern Physics

Read Explanation

Magnetism and Electromagnetic Induction

Read Explanation

Measurements

Read Explanation

Oscillations

Read Explanation

Astrophysics

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