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

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}

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

Use the Product to a Power Property,

${(6 a)}^{0} = 6^{0} a^{0} = 1 \cdot 1 = 1$

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

Use the Product to a Power Property and simplify.

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

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

Apply the concept of power product.

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

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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

Step by step solution

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

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

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

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

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In the following exercises, simplify each expression using the Product to a Power Property.(a)-3xy2(b)6a0(c)5x2-2(d)-4y-32

Short Answer

Step by step solution

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

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

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

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

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Applied Mathematics

Study anywhere. Anytime. Across all devices.

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