Chapter 5: Q 121. (page 521)

In the following exercises, simplify each expression using the Product to a Power Property.
$(a) . {(- 5 a b)}^{3} (b) . {(- 4 p q)}^{0} (c) . {(- 6 x^{3})}^{- 2} (d) . {(3 y^{- 4})}^{2}$

Short Answer

Expert verified

The simplified form is

$(a) . {(- 5 a b)}^{3} = - 125 a^{3} b^{3} (b) . (- 4 p q) 0 = 1 (c) . {(- 6 x^{3})}^{- 2} = \frac{1}{36 x^{6}} (d) . {(3 y^{- 4})}^{2} = \frac{9}{y^{8}}$

Step by step solution

Part (a) Step 1. The given expression is -5ab3

Given, ${(- 5 a b)}^{3}$

Now apply product to a power property

We get,

${(- 5)}^{3} \cdot a^{3} \cdot b^{3} = - 125 a^{3} b^{3}$

Part (b) Step 1. The given expression is -4pq0

Given, ${(- 4 p q)}^{0}$

Zero exponent property $a^{0} = 1$

We get,

${(- 4 p q)}^{0} = 1$

Part (c) Step 1. The given expression is -6x3-2

Given, ${(- 6 x^{3})}^{- 2}$

First of all, apply product to a power property

We get,

${(- 6)}^{- 2} \cdot {(x^{3})}^{- 2}$

Now, apply properties of Negative exponents $a^{- n} = \frac{1}{n}$

We get,

$\frac{1}{{(- 6)}^{2}} \cdot \frac{1}{{(x^{3})}^{2}} = \frac{1}{36} \cdot \frac{1}{x^{6}} = \frac{1}{36 x^{6}}$

Part (d) Step 1. The given expression is 3y-42

Given, ${(3 y^{- 4})}^{2}$

First of all, apply product to a power property

We get,

$3^{2} \cdot {(y^{- 4})}^{2} = 9 \cdot {(y^{- 4})}^{2}$

Now, apply power property ${(a^{m})}^{n} = a^{m \cdot n}$

We get,

$9 \cdot {(y)}^{- 8} = 9 \cdot \frac{1}{y^{8}} = \frac{9}{y^{8}}$

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In the following exercises, simplify each expression using the Product to a Power Property.
$(a) . {(- 5 a b)}^{3} (b) . {(- 4 p q)}^{0} (c) . {(- 6 x^{3})}^{- 2} (d) . {(3 y^{- 4})}^{2}$

Short Answer

Step by step solution

Part (a) Step 1. The given expression is -5ab3

Part (b) Step 1. The given expression is -4pq0

Part (c) Step 1. The given expression is -6x3-2

Part (d) Step 1. The given expression is 3y-42

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In the following exercises, simplify each expression using the Product to a Power Property.a.-5ab3b.-4pq0c.-6x3-2d.3y-42

Short Answer

Step by step solution

Part (a) Step 1. The given expression is -5ab3

Part (b) Step 1. The given expression is -4pq0

Part (c) Step 1. The given expression is -6x3-2

Part (d) Step 1. The given expression is 3y-42

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

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Study anywhere. Anytime. Across all devices.

In the following exercises, simplify each expression using the Product to a Power Property.
$(a) . {(- 5 a b)}^{3} (b) . {(- 4 p q)}^{0} (c) . {(- 6 x^{3})}^{- 2} (d) . {(3 y^{- 4})}^{2}$