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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

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

01

a. The given expression is -4ab2

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

Now, apply product to a power property

We get,

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

02

b. The given expression is 5x0

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

Now, apply zero exponent property

We get,

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

03

c. The given expression is 4y3-3

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

Apply product to the power property

We get,

${(4)}^{- 3} 路 {(y^{3})}^{- 3}$

Now, apply properties of negative exponents

We get,

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

Now, apply power property

We get,

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

04

d. The given expression is -7y-32

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

First of all, apply product to a power property

We get,

${(- 7)}^{2} 路 {(y^{- 3})}^{2}$

Now, apply power property and property of negative exponents

We get,

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

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Most popular questions from this chapter

Solve the square using the binomial squares pattern.

${(\frac{1}{5} x - \frac{1}{7} y)}^{2}$

Multiply (a) $(3 脳 10^{- 5}) (3 脳 10^{9})$ to get answer in decimal form

Divide (b) $\frac{7 脳 10^{- 3}}{1 脳 10^{- 7}}$ to get answer in decimal form

In the following exercises, multiply the binomials. Use any method.

$(x + 8) (x + 3)$

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