Chapter 5: Q. 122. (page 521)

In the following exercises, simplify each expression using the Product to a Power Property.
$(a) . {(- 3 x y z)}^{4} (b) . {(- 7 m n)}^{0} (c) . {(- 3 x^{3})}^{- 2} (d) . {(2 y^{- 5})}^{2}$

Short Answer

Expert verified

The simplified form of the expressions

$(a) . {(- 3 x y z)}^{4} = 81 x^{4} y^{4} z^{4} (b) . {(- 7 m n)}^{0} = 1 (c) . {(- 3 x^{3})}^{- 2} = \frac{1}{9 x^{6}} (d) . {(2 y^{- 5})}^{2} = \frac{4}{y^{10}}$

Step by step solution

Part (a) Step 1. Given information.

The given expression is (-3xyz)⁴.

Part (a) Step 2. Calculation of expression:

In calculation of expression we use concept of product of power-

(ab)ⁿ = aⁿ bⁿ

So,

(-3xyz)⁴ = 81x⁴y⁴z⁴.

Part (b) Sep 1. Given information.

The given expression is (-7mn)⁰.

Part (b) Step 2. Calculation of expression.

Calculate the expression by anything raised to zero is always 1.

So,

(-7mn)⁰= 1.

Part (c) Step 1. Given information.

The given expression is (-3x³)^-2.

Part (c) Step 2. Calculation of expression.

Calculate the expression by negative exponent and product of power.

product of power-

(ab)ⁿ = aⁿ bⁿ

product of negative exponent-

(ab)^-n = 1/(ab)ⁿ

We get,

(-3x³)^-2 = $\frac{1}{{(- 3 x^{3})}^{2}}$

= $\frac{1}{9 x^{6}}$

Part (d) Step 1. Given information.

The given expression is (2y^-5)².

Part (d) Step 2. Calculate the expression.

Apply the concept of power product-

(ab)ⁿ = aⁿ bⁿ

So,

(2y^-5)² = 4y^-10

= $\frac{4}{y^{10}}$

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.

In the following exercises, simplify each expression using the Product to a Power Property.
$(a) . {(- 3 x y z)}^{4} (b) . {(- 7 m n)}^{0} (c) . {(- 3 x^{3})}^{- 2} (d) . {(2 y^{- 5})}^{2}$

Short Answer

Step by step solution

Part (a) Step 1. Given information.

Part (a) Step 2. Calculation of expression:

Part (b) Sep 1. Given information.

Part (b) Step 2. Calculation of expression.

Part (c) Step 1. Given information.

Part (c) Step 2. Calculation of expression.

Part (d) Step 1. Given information.

Part (d) Step 2. Calculate the expression.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Discrete Mathematics

Mechanics Maths

Calculus

Logic and Functions

Probability and Statistics

Study anywhere. Anytime. Across all devices.

In the following exercises, simplify each expression using the Product to a Power Property.a.-3xyz4b.-7mn0c.-3x3-2d.2y-52

Short Answer

Step by step solution

Part (a) Step 1. Given information.

Part (a) Step 2. Calculation of expression:

Part (b) Sep 1. Given information.

Part (b) Step 2. Calculation of expression.

Part (c) Step 1. Given information.

Part (c) Step 2. Calculation of expression.

Part (d) Step 1. Given information.

Part (d) Step 2. Calculate the expression.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Discrete Mathematics

Mechanics Maths

Calculus

Logic and Functions

Probability and Statistics

Study anywhere. Anytime. Across all devices.

In the following exercises, simplify each expression using the Product to a Power Property.
$(a) . {(- 3 x y z)}^{4} (b) . {(- 7 m n)}^{0} (c) . {(- 3 x^{3})}^{- 2} (d) . {(2 y^{- 5})}^{2}$