Chapter 5: Q 120. (page 521)

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

Short Answer

Expert verified

The simplified form of the expressions

$(a) . {(- 4 a b)}^{2} = 16 a^{2} b^{2} (b) . {(5 x)}^{0} = 1 (c) . {(4 y^{3})}^{- 3} = \frac{1}{64 y^{9}} (d) . {(- 7 y^{- 3})}^{2} = \frac{49}{y^{6}}$

Step by step solution

a. The given expression is -4ab2

Given, ${(- 4 a b)}^{2}$

Now, apply product to a power property

We get,

${(- 4)}^{2} \cdot a^{2} \cdot b^{2} = 16 a^{2} b^{2}$

b. The given expression is 5x0

Given, ${(5 x)}^{0}$

Now, apply zero exponent property

We get,

${(5 x)}^{0} = 1$

c. The given expression is 4y3-3

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

Apply product to the power property

We get,

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

Now, apply properties of negative exponents

We get,

$\frac{1}{4^{3}} \cdot \frac{1}{{(y^{3})}^{3}}$

Now, apply power property

We get,

$\frac{1}{64} \cdot \frac{1}{y^{9}} = \frac{1}{64 y^{9}}$

d. The given expression is -7y-32

Given, ${(- 7 y^{- 3})}^{2}$

First of all, apply product to a power property

We get,

${(- 7)}^{2} \cdot {(y^{- 3})}^{2}$

Now, apply power property and property of negative exponents

We get,

$49 \cdot {(y)}^{- 6} = 49 \cdot \frac{1}{y^{6}} = \frac{49}{y^{6}}$

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

Short Answer

Step by step solution

a. The given expression is -4ab2

b. The given expression is 5x0

c. The given expression is 4y3-3

d. The given expression is -7y-32

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In the following exercises, simplify each expression using the Product to a Power Property.a.-4ab2b.5x0c.4y3-3d.-7y-32

Short Answer

Step by step solution

a. The given expression is -4ab2

b. The given expression is 5x0

c. The given expression is 4y3-3

d. The given expression is -7y-32

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Geometry

Theoretical and Mathematical Physics

Logic and Functions

Applied Mathematics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

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