Chapter 5: Q. 103 (page 520)

Use the Definition of a Negative Exponent In the following exercises, simplify each expression.
$(a) {(\frac{4}{9})}^{- 3} (b) {(- \frac{u}{v})}^{- 5}$

Short Answer

Expert verified

The simplified expressions are:

$(a) {(\frac{4}{9})}^{- 3} = \frac{729}{64} (b) {(- \frac{u}{v})}^{- 5} = - \frac{v^{5}}{u^{5}}$

Step by step solution

Step 1. Property for negative exponent

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

$a^{- n} = \frac{1}{a^{n}} o r \frac{1}{a^{- n}} = a^{n}$

Part a Step 1. Given information

The given expression is ${(\frac{4}{9})}^{- 3}$ .

We have to simplify the expression using property for negative exponents.

Part a Step 2. Simplify

Using property for negative exponents,

$\begin{matrix} {(\frac{4}{9})}^{- 3} = {(\frac{9}{4})}^{3} \\ = \frac{729}{64} \end{matrix}$

So, the simplified expression is ${(\frac{4}{9})}^{- 3} = \frac{729}{64}$

Part b Step 1. Given information

The given expression is ${(- \frac{u}{v})}^{- 5}$ .

We have to simplify the expression using property for negative exponents.

Part b Step 2.Simplify

Using property for negative exponents,

$\begin{matrix} {(- \frac{u}{v})}^{- 5} = {(- \frac{v}{u})}^{5} \\ = - \frac{v^{5}}{u^{5}} \end{matrix}$

So, the simplified expression is ${(- \frac{u}{v})}^{- 5} = - \frac{v^{5}}{u^{5}}$

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Use the Definition of a Negative Exponent In the following exercises, simplify each expression.
$(a) {(\frac{4}{9})}^{- 3} (b) {(- \frac{u}{v})}^{- 5}$

Short Answer

Step by step solution

Step 1. Property for negative exponent

Part a Step 1. Given information

Part a Step 2. Simplify

Part b Step 1. Given information

Part b Step 2.Simplify

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Use the Definition of a Negative Exponent In the following exercises, simplify each expression.a49-3b-uv-5

Short Answer

Step by step solution

Step 1. Property for negative exponent

Part a Step 1. Given information

Part a Step 2. Simplify

Part b Step 1. Given information

Part b Step 2.Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Discrete Mathematics

Theoretical and Mathematical Physics

Geometry

Logic and Functions

Pure Maths

Study anywhere. Anytime. Across all devices.

Use the Definition of a Negative Exponent In the following exercises, simplify each expression.
$(a) {(\frac{4}{9})}^{- 3} (b) {(- \frac{u}{v})}^{- 5}$