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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 119. (page 521)

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

Short Answer

Expert verified

$Part (a) 9 x^{2} y^{2} Part (b) 1 Part (c) \frac{1}{25 x^{4}} Part (d) \frac{16}{y^{6}}$

Step by step solution

01

Part (a) Step 1. Simplify the given expression.

In the given expression, we will use the Product to a Power Property,

${(- 3 x y)}^{2} = {(- 3)}^{2} x^{2} y^{2}$

Simplify,

9 x^{2} y^{2}

02

Part (b) Step 1. Simplify the given expression.

Use the Product to a Power Property,

${(6 a)}^{0} = 6^{0} a^{0} = 1 路 1 = 1$

03

Part (c) Step 1. Simplify the given expression.

Use the Product to a Power Property and simplify.

${(5 x^{2})}^{- 2} = {(5)}^{- 2} {(x^{2})}^{- 2} = \frac{1}{5^{2}} 路 \frac{1}{{(x^{2})}^{2}} = \frac{1}{25 x^{4}}$

04

Part (d) Step 1. Simplify the given expression.

Apply the concept of power product.

${(- 4 y^{- 3})}^{2} = {(- 4)}^{2} {(y^{- 3})}^{2} = 16 y^{- 3 路 2} = 16 y^{- 6} = 16 路 \frac{1}{y^{6}} = \frac{16}{y^{6}}$

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Most popular questions from this chapter

When you convert a number from decimal notation to scientific notation, how do you know if the exponent will be positive or negative

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