Q. 122. In the following exercises, simp... [FREE SOLUTION]

91影视

Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

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

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

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91影视

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.

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91影视

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.

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Study anywhere. Anytime. Across all devices.

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