Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 5: Q. 5.29 (page 507)

Simplify each expression:
$鈸� z^{鈭� 3} 鈸� 10^{鈭� 7} 鈸� \frac{1}{p^{鈭� 8}} 鈸� \frac{1}{4^{鈭� 3}}$

Short Answer

Expert verified

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

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

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

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

Step by step solution

Step 1. Given Information

In the given question we have to simplify each expression:

$鈸� z^{鈭� 3} 鈸� 10^{鈭� 7} 鈸� \frac{1}{p^{鈭� 8}} 鈸� \frac{1}{4^{鈭� 3}}$

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

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

$z^{鈭� 3} = \frac{1}{z^{3}}$

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

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

$10^{鈭� 7} = \frac{1}{10^{7}}$

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

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

$\frac{1}{p^{鈭� 8}} = p^{8}$

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

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

$\frac{1}{4^{鈭� 3}} = 4^{3} \frac{1}{4^{鈭� 3}} = 64$

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91影视

Simplify each expression:
$鈸� z^{鈭� 3} 鈸� 10^{鈭� 7} 鈸� \frac{1}{p^{鈭� 8}} 鈸� \frac{1}{4^{鈭� 3}}$

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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91影视

Simplify each expression:鈸�z鈭�3鈸�10鈭�7鈸�1p鈭�8鈸�14鈭�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

Calculus

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Probability and Statistics

Statistics

Study anywhere. Anytime. Across all devices.

Simplify each expression:
$鈸� z^{鈭� 3} 鈸� 10^{鈭� 7} 鈸� \frac{1}{p^{鈭� 8}} 鈸� \frac{1}{4^{鈭� 3}}$