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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) (-4ab)²
(b) (5x)⁰
(c) (4y³)^-3
(d) (-7y^-3)²

Short Answer

Expert verified

The simplified form of the given expression is :-

$(a) 16 a^{2} b^{2} (b) 1 (c) \frac{1}{64 y^{9}} (d) 49 y^{- 6}$

Step by step solution

01

Part (a) Step 1. Given information.

The given expression is ${(- 4 a b)}^{2}$ .

02

Part (a). Step 2. Apply the power rule.

Here we use the concept of power rule,

${(a b)}^{n} = a^{n} b^{n}$

So,

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

03

Part (b) Step 1. Given information.

The given expression is ${(5 x)}^{0} .$

04

part (b). Step2. Apply the concept.

Here we apply the concept of anything raised to zero is $1$ .

So,

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

05

Part (c) Step 1. Given information.

The given expression is ${(4 y^{3})}^{- 3} .$

06

Part (c) Step 2. We apply the concept.

In this expression we use negative exponents rule that is-

$b^{- n} = \frac{1}{b^{n}} .$

Our final expression is $\frac{1}{64 y^{9}} .$

07

Part (d) step 1. Given information.

The given expression is ${(- 7 y^{- 3})}^{2} .$

08

Part (d) Step 2. Apply the concept.

We use the concept of negative exponents.

${(- a b)}^{2} = a^{2} b^{2} .$

So,

${(- 7 y^{- 3})}^{2} = 49 y^{- 6}$

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