Chapter 5: Q. 104 (page 520)

Use the definition of a Negative Exponent to simplify $(a) {(\frac{7}{2})}^{- 3} (b) {(- \frac{3}{x})}^{- 3}$ .

Short Answer

Expert verified

The simplified equation is $(a) \frac{8}{343} (b) - \frac{x^{3}}{27} .$

Step by step solution

Part a Step 1. Given information

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

We have to simplify the expression.

Part a Step 2. Definition of Negative Exponent.

If $n$ is an integer and $a \neq 0$ , then

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

Part a. Step 3. Simplify the expression.

Using the definition of Negative exponent

${(\frac{7}{2})}^{- 3} = {(\frac{2}{7})}^{3} = \frac{8}{343}$

So, ${(\frac{7}{2})}^{- 3} = \frac{8}{343} .$

Part b. Step 1. Given information.

The given expression is ${(- \frac{3}{x})}^{- 3}$ .

We have to simplify the expression.

Part (b). Step 2. Definition of Negative Exponents.

If $n$ is an integer and $a \neq 0,$ then

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

Part (b). Step 3. Simplify the expression.

Using the definition of Negative exponent

${(- \frac{3}{x})}^{- 3} = {(- \frac{x}{3})}^{3} = - \frac{x^{3}}{27} .$

So, ${(- \frac{3}{x})}^{- 3} = - \frac{x^{3}}{27} .$

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Use the definition of a Negative Exponent to simplify $(a) {(\frac{7}{2})}^{- 3} (b) {(- \frac{3}{x})}^{- 3}$ .

Short Answer

Step by step solution

Part a Step 1. Given information

Part a Step 2. Definition of Negative Exponent.

Part a. Step 3. Simplify the expression.

Part b. Step 1. Given information.

Part (b). Step 2. Definition of Negative Exponents.

Part (b). Step 3. Simplify the expression.

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Use the definition of a Negative Exponent to simplify(a)72-3(b)-3x-3.

Short Answer

Step by step solution

Part a Step 1. Given information

Part a Step 2. Definition of Negative Exponent.

Part a. Step 3. Simplify the expression.

Part b. Step 1. Given information.

Part (b). Step 2. Definition of Negative Exponents.

Part (b). Step 3. Simplify the expression.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Mechanics Maths

Applied Mathematics

Theoretical and Mathematical Physics

Discrete Mathematics

Decision Maths

Study anywhere. Anytime. Across all devices.

Use the definition of a Negative Exponent to simplify $(a) {(\frac{7}{2})}^{- 3} (b) {(- \frac{3}{x})}^{- 3}$ .