Chapter 6: Q. 121 (page 710)

In the following exercises, simplify each expression using the Product to a Power Property.
$ⓐ {(- 7 n)}^{3} ⓑ {(3 x y z)}^{4}$

Short Answer

Expert verified

(a) The value of ${(- 7 n)}^{3} = {- 343 n}^{3}$ .

(b) The value of ${(3 x y z)}^{4} = 81 x^{4} y^{4} z^{4}$ .

Step by step solution

Step 1. Given Information

In the following exercises, we have to simplify given expression using the Product to a Power Property.
$ⓐ {(- 7 n)}^{3} ⓑ {(3 x y z)}^{4}$

Part (a) Step 1. Given expression is (−7n)3

Use Power of a Product Property, ${(a b)}^{m} = a^{m} b^{m}$

${(- 7 n)}^{3} = {{(- 7)}^{3} \cdot (n)}^{3}$

Simplify.

${(- 7 n)}^{3} = {- 343 n}^{3}$

Part (b) Step 1. Given expression is (3xyz)4

Use Power of a Product Property, ${(a b)}^{m} = a^{m} b^{m}$

${(3 x y z)}^{4} = {{(3)}^{4} {(x)}^{4} {(y)}^{4} (z)}^{4}$

Simplify.

${(3 x y z)}^{4} = 81 x^{4} y^{4} z^{4}$

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In the following exercises, simplify each expression using the Product to a Power Property.
$ⓐ {(- 7 n)}^{3} ⓑ {(3 x y z)}^{4}$

Short Answer

Step by step solution

Step 1. Given Information

Part (a) Step 1. Given expression is (−7n)3

Part (b) Step 1. Given expression is (3xyz)4

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In the following exercises, simplify each expression using the Product to a Power Property.ⓐ(−7n)3ⓑ(3xyz)4

Short Answer

Step by step solution

Step 1. Given Information

Part (a) Step 1. Given expression is (−7n)3

Part (b) Step 1. Given expression is (3xyz)4

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Statistics

Theoretical and Mathematical Physics

Decision Maths

Pure Maths

Geometry

Study anywhere. Anytime. Across all devices.

In the following exercises, simplify each expression using the Product to a Power Property.
$ⓐ {(- 7 n)}^{3} ⓑ {(3 x y z)}^{4}$