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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. 107 (page 520)

Use the definition of Negative Exponent to simplify (a) $3 路 5^{- 1}$ (b) ${(3 路 5)}^{- 1} .$

Short Answer

Expert verified

The simplified equation is (a) $\frac{3}{5}$ (b) $\frac{1}{15} .$

Step by step solution

01

Part (a). Step 1. Given information.

The given expression is $3 路 5^{- 1}$ .

We have to simplify the expression.

02

Part (a). Step 2. Definition of Negative exponents.

If $n$ is an integer and $a 鈮� 0$ , then

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

03

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

Using the definition of Negative exponents

$3 路 5^{- 1} = 3 路 \frac{1}{5} = \frac{3}{5}$

So, $3 路 5^{- 1} = \frac{3}{5} .$

04

Part (b). Step 1. Given information.

The given expression is ${(3 路 5)}^{- 1}$ .

We have to simplify the expression.

05

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

If $n$ is an integer and $a 鈮� 0$ then

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

06

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

Using the definition of Negative Exponents

${(3 路 5)}^{- 1} = (\frac{1}{3} 路 \frac{1}{5}) = \frac{1}{15}$ .

So, ${(3 路 5)}^{- 1} = \frac{1}{15} .$

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Most popular questions from this chapter

In the following exercises, multiply the binomials. Use any method.

$(2 t - 9) (10 t + 1)$

Multiply (a) $(3.5 脳 10^{- 4}) (1.6 脳 10^{- 2})$ to get answer in decimal form

Divide (b) $\frac{8 脳 10^{6}}{4 脳 10^{- 1}}$ to get answer in decimal form

Multiply (a) $(3 脳 10^{- 5}) (3 脳 10^{9})$ to get answer in decimal form

Divide (b) $\frac{7 脳 10^{- 3}}{1 脳 10^{- 7}}$ to get answer in decimal form

Multiply: (a) $(5 y^{7}) (- 7 y^{4})$

(b) $(\frac{2}{5} a^{4} b^{3}) (15 a b^{3})$ .

Simplify ${(\frac{1}{3} m^{3} n^{2})}^{4} {(9 m^{8} n^{3})}^{2}$

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