Q.92 In the following exercises, simp... [FREE SOLUTION]

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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.92 (page 520)

In the following exercises, simplify each expression using the properties for exponents.
$(a) \frac{u^{24}}{u^{3}} (b) \frac{9^{15}}{9^{5}} (c) \frac{x}{x^{7}} (d) \frac{10}{10^{3}}$

Short Answer

Expert verified

The simplified form is:

$(a) \frac{u^{24}}{u^{3}} = u^{21} (b) \frac{9^{15}}{9^{5}} = 9^{10} (c) \frac{x}{x^{7}} = \frac{1}{x^{6}} (d) \frac{10}{10^{3}} = \frac{1}{100}$

Step by step solution

Step 1

Some properties of exponents are:

$\frac{a^{m}}{a^{n}} = a^{m - n}, m > n \frac{a^{m}}{a^{n}} = \frac{1}{a^{n - m}}, n > m$

Step 2

Use the property $\frac{a^{m}}{a^{n}} = a^{m - n}, m > n$ to simplify the expressions:

$\begin{array}{rcl} (a) \frac{u^{24}}{u^{3}} & = & u^{24 - 3} \\ = & u^{21} \\ (b) \frac{9^{15}}{9^{5}} & = & 9^{15 - 5} \\ = & 9^{10} \end{array}$

Step 3

Use the property that $\frac{a^{m}}{a^{n}} = \frac{1}{a^{n - m}}, n > m$ to simplify the expressions:

$\begin{array}{rcl} (c) \frac{x}{x^{7}} & = & \frac{x^{1}}{x^{7}} \\ = & \frac{1}{x^{7 - 1}} \\ = & \frac{1}{x^{6}} \\ (d) \frac{10}{10^{3}} & = & \frac{10^{1}}{10^{3}} \\ = & \frac{1}{10^{3 - 1}} \\ = & \frac{1}{10^{2}} \\ = & \frac{1}{100} \end{array}$

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91影视

In the following exercises, simplify each expression using the properties for exponents.
$(a) \frac{u^{24}}{u^{3}} (b) \frac{9^{15}}{9^{5}} (c) \frac{x}{x^{7}} (d) \frac{10}{10^{3}}$

Short Answer

Step by step solution

Step 1

Step 2

Step 3

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91影视

In the following exercises, simplify each expression using the properties for exponents.au24u3b91595cxx7d10103

Short Answer

Step by step solution

Step 1

Step 2

Step 3

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Statistics

Geometry

Logic and Functions

Applied Mathematics

Pure Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, simplify each expression using the properties for exponents.
$(a) \frac{u^{24}}{u^{3}} (b) \frac{9^{15}}{9^{5}} (c) \frac{x}{x^{7}} (d) \frac{10}{10^{3}}$