Chapter 5: Q. 5.29 (page 507)

Simplify each expression:
$ⓐ z^{- 3} ⓑ 10^{- 7} ⓒ \frac{1}{p^{- 8}} ⓓ \frac{1}{4^{- 3}}$

Short Answer

Expert verified

The simplified expression of $z^{- 3} = \frac{1}{z^{3}}$

The simplified expression of $10^{- 7} = \frac{1}{10^{7}}$

The simplified expression of $\frac{1}{p^{- 8}} = p^{8}$

The simplified expression of $\frac{1}{4^{- 3}} = 64$

Step by step solution

Step 1. Given Information

In the given question we have to simplify each expression:

$ⓐ z^{- 3} ⓑ 10^{- 7} ⓒ \frac{1}{p^{- 8}} ⓓ \frac{1}{4^{- 3}}$

Part (a) Step 1. The given expression is z−3

Using the definition of a negative exponent, $a^{- n} = \frac{1}{a^{n}}$

$z^{- 3} = \frac{1}{z^{3}}$

Part (b) Step 1. The given expression is 10−7

Using the definition of a negative exponent, $a^{- n} = \frac{1}{a^{n}}$

$10^{- 7} = \frac{1}{10^{7}}$

Part (c) Step 1. The given expression is 1p−8

Using the definition of a negative exponent, $\frac{1}{a^{n}} = a^{- n}$

$\frac{1}{p^{- 8}} = p^{8}$

Part (d) Step 1. The given expression is 14−3

Using the definition of a negative exponent, $\frac{1}{a^{n}} = a^{- n}$

$\frac{1}{4^{- 3}} = 4^{3} \frac{1}{4^{- 3}} = 64$

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Simplify each expression:
$ⓐ z^{- 3} ⓑ 10^{- 7} ⓒ \frac{1}{p^{- 8}} ⓓ \frac{1}{4^{- 3}}$

Short Answer

Step by step solution

Step 1. Given Information

Part (a) Step 1. The given expression is z−3

Part (b) Step 1. The given expression is 10−7

Part (c) Step 1. The given expression is 1p−8

Part (d) Step 1. The given expression is 14−3

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Simplify each expression:ⓐz−3ⓑ10−7ⓒ1p−8ⓓ14−3

Short Answer

Step by step solution

Step 1. Given Information

Part (a) Step 1. The given expression is z−3

Part (b) Step 1. The given expression is 10−7

Part (c) Step 1. The given expression is 1p−8

Part (d) Step 1. The given expression is 14−3

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

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Study anywhere. Anytime. Across all devices.

Simplify each expression:
$ⓐ z^{- 3} ⓑ 10^{- 7} ⓒ \frac{1}{p^{- 8}} ⓓ \frac{1}{4^{- 3}}$