Chapter 5: Q. 102 (page 520)

Use the Definition of a Negative Exponent In the following exercises, simplify each expression.
$(a) {(\frac{3}{10})}^{- 2} (b) {(- \frac{2}{z})}^{- 3}$

Short Answer

Expert verified

The simplified expressions are:

$(a) {(\frac{3}{10})}^{- 2} = \frac{100}{9} (b) {(- \frac{2}{z})}^{- 3} = - \frac{z^{3}}{8}$

Step by step solution

Step 1. Property for negative exponents

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 ${(\frac{3}{10})}^{- 2}$ .

We have to simplify the expression using negative exponents.

Part a Step 2. Simplify

Using the property for negative exponents,

$\begin{matrix} {(\frac{3}{10})}^{- 2} = {(\frac{10}{3})}^{2} \\ = \frac{100}{9} \end{matrix}$

So, the simplified expression is ${(\frac{3}{10})}^{- 2} = \frac{100}{9}$

Part b Step 1. Given information

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

We have to simplify the expression using negative exponents.

Part b Step 2. Simplify

Using the property for negative exponents,

$\begin{matrix} {(- \frac{2}{z})}^{- 3} = {(- \frac{z}{2})}^{3} \\ = - \frac{z^{3}}{8} \end{matrix}$

So, the simplified expression is ${(- \frac{2}{z})}^{- 3} = - \frac{z^{3}}{8}$

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Use the Definition of a Negative Exponent In the following exercises, simplify each expression.
$(a) {(\frac{3}{10})}^{- 2} (b) {(- \frac{2}{z})}^{- 3}$

Short Answer

Step by step solution

Step 1. Property for negative exponents

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.a310-2b-2z-3

Short Answer

Step by step solution

Step 1. Property for negative exponents

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

Discrete Mathematics

Geometry

Statistics

Decision Maths

Theoretical and Mathematical Physics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Use the Definition of a Negative Exponent In the following exercises, simplify each expression.
$(a) {(\frac{3}{10})}^{- 2} (b) {(- \frac{2}{z})}^{- 3}$