Chapter 11: Q. 8.58 (page 1069)

Simplify:
(a) ${(- 256)}^{\frac{1}{4}}$
(b) ${- 256}^{\frac{1}{4}}$
(c) ${(256)}^{- \frac{1}{4}}$

Short Answer

Expert verified

The simplification of ${(- 256)}^{\frac{1}{4}}$ has no real root

The simplification of $- 256^{\frac{1}{4}}$ is $- 4$

The simplification of ${(256)}^{\frac{1}{4}}$ is $\frac{1}{4}$

Step by step solution

Part (a) Step 1. Given

The expression is ${(- 256)}^{\frac{1}{4}}$

To simplify the expression.

Part (a) Step 2. Rewrite as the nth root

Rewrite as the fourth root.

${(- 256)}^{\frac{1}{4}} = \sqrt[4]{- 256}$

$= \sqrt[4]{{(- 4)}^{4}}$

It has no real root.

Part (b) Step 1. Given

The expression is $- 256^{\frac{1}{4}}$

To simplify the expression.

Part (b) Step 2. Rewrite as the nth root

Rewrite as the fourth root

$- 256^{\frac{1}{4}} = - \sqrt[4]{256}$

The root is only for $256$ . So,

$= - \sqrt[4]{4^{4}}$

$= - 4$

Part (c) Step 1. Given

The expression is ${(256)}^{- \frac{1}{4}}$

To simplify the expression.

Part (c) Step 2. Rewrite as the nth root

Rewrite using the property, $a^{- n} = \frac{1}{a^{n}}$

${(256)}^{- \frac{1}{4}} = \frac{1}{(256)}$ ¹⁴

Rewrite as the fourth root

$= \frac{1}{\sqrt[4]{4^{4}}}$

$= \frac{1}{4}$

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) ${(- 256)}^{\frac{1}{4}}$
(b) ${- 256}^{\frac{1}{4}}$
(c) ${(256)}^{- \frac{1}{4}}$

Short Answer

Step by step solution

Part (a) Step 1. Given

Part (a) Step 2. Rewrite as the nth root

Part (b) Step 1. Given

Part (b) Step 2. Rewrite as the nth root

Part (c) Step 1. Given

Part (c) Step 2. Rewrite as the nth root

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Decision Maths

Discrete Mathematics

Theoretical and Mathematical Physics

Logic and Functions

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Simplify:(a)(-256)14(b)-25614(c) (256)-14

Short Answer

Step by step solution

Part (a) Step 1. Given

Part (a) Step 2. Rewrite as the nth root

Part (b) Step 1. Given

Part (b) Step 2. Rewrite as the nth root

Part (c) Step 1. Given

Part (c) Step 2. Rewrite as the nth root

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Decision Maths

Discrete Mathematics

Theoretical and Mathematical Physics

Logic and Functions

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Simplify:
(a) ${(- 256)}^{\frac{1}{4}}$
(b) ${- 256}^{\frac{1}{4}}$
(c) ${(256)}^{- \frac{1}{4}}$