Chapter 8: Q 140E (page 768)

In the following exercises, simplify.
Part (a): ${(- 32)}^{\frac{1}{5}}$
Part (b): ${(243)}^{- \frac{1}{5}}$
Part (c): $- 125^{\frac{1}{3}}$

Short Answer

Expert verified

Part (a): On simplifying, we know the solution is not real.

Part (b): On simplifying, we get $\frac{1}{3}$ .
Part (c): On simplifying, we get $- 5$ .

Step by step solution

Part (a) Step 1. Rewrite as a root.

Consider the given question,

${(- 32)}^{\frac{1}{5}}$

Rewrite as a fifth root,

$= \sqrt[5]{(- 32)}$

On simplifying the expression,

$= \sqrt[5]{{(- 2)}^{5}}$

The solution is not real.

Part (b) Step 1. Rewrite as a root.

Consider the given question,

${(243)}^{- \frac{1}{5}}$

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

$= \frac{1}{{(243)}^{\frac{1}{5}}}$

Rewrite as a fifth root,

$= \frac{1}{\sqrt[5]{(243)}}$

On simplifying the expression,

$= \frac{1}{\sqrt[5]{3^{5}}} = \frac{1}{3}$

Part (c) Step 1. Rewrite as a root.

Consider the given question,

$- 125^{\frac{1}{3}}$

The exponent only applies to the $125$ .

Rewrite as a cube root,

$= - \sqrt[3]{125}$

On simplifying the expression,

$= - \sqrt[3]{5^{3}} = - 5$

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In the following exercises, simplify.
Part (a): ${(- 32)}^{\frac{1}{5}}$
Part (b): ${(243)}^{- \frac{1}{5}}$
Part (c): $- 125^{\frac{1}{3}}$

Short Answer

Step by step solution

Part (a) Step 1. Rewrite as a root.

Part (b) Step 1. Rewrite as a root.

Part (c) Step 1. Rewrite as a root.

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In the following exercises, simplify.Part (a):-3215Part (b):243-15Part (c):-12513

Short Answer

Step by step solution

Part (a) Step 1. Rewrite as a root.

Part (b) Step 1. Rewrite as a root.

Part (c) Step 1. Rewrite as a root.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Decision Maths

Mechanics Maths

Geometry

Applied Mathematics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises, simplify.
Part (a): ${(- 32)}^{\frac{1}{5}}$
Part (b): ${(243)}^{- \frac{1}{5}}$
Part (c): $- 125^{\frac{1}{3}}$