Chapter 5: Q. 105 (page 520)

Use the definition of Negative Exponents to simplify (a) ${(- 5)}^{- 2}$ (b) $- 5^{- 2}$ (c) ${(- \frac{1}{5})}^{- 2}$ (d) $- {(\frac{1}{5})}^{- 2}$

Short Answer

Expert verified

The simplified expression is (a) $\frac{1}{25}$ (b) $- \frac{1}{25}$ (c) $25$ (d) $- 25$

Step by step solution

Part (a). Step 1. Given information.

The given expression is ${(- 5)}^{- 2}$ .

We have to simplify the equation.

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

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

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

So, ${(- 5)}^{- 2} = \frac{1}{25} .$

Part (b). Step 1. Given information.

The given expression is $- 5^{- 2}$ .

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 exponents

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

So, $- 5^{- 2} = - \frac{1}{25}$ .

Part (c). Step 1. Given information.

The given expression is ${(- \frac{1}{5})}^{- 2}$ .

We have to simplify the expression.

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

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

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

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

Using the definition of Negative Exponents

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

So, ${(- \frac{1}{5})}^{- 2} = 25 .$

Part (d). Step 1. Given information.

The given expression is $- {(\frac{1}{5})}^{- 2}$ .

We have to simplify the expression.

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

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

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

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

Using the definition of Negative exponents

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

So, $- {(\frac{1}{5})}^{- 2} = - 25 .$

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Use the definition of Negative Exponents to simplify (a) ${(- 5)}^{- 2}$ (b) $- 5^{- 2}$ (c) ${(- \frac{1}{5})}^{- 2}$ (d) $- {(\frac{1}{5})}^{- 2}$

Short Answer

Step by step solution

Part (a). Step 1. Given information.

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

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.

Part (c). Step 1. Given information.

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

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

Part (d). Step 1. Given information.

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

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

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Use the definition of Negative Exponents to simplify (a)-5-2(b)-5-2(c)-15-2(d)-15-2

Short Answer

Step by step solution

Part (a). Step 1. Given information.

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

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.

Part (c). Step 1. Given information.

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

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

Part (d). Step 1. Given information.

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

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

One App. One Place for Learning.

Most popular questions from this chapter

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Study anywhere. Anytime. Across all devices.

Use the definition of Negative Exponents to simplify (a) ${(- 5)}^{- 2}$ (b) $- 5^{- 2}$ (c) ${(- \frac{1}{5})}^{- 2}$ (d) $- {(\frac{1}{5})}^{- 2}$