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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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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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

Mechanics Maths

Pure Maths

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Logic and Functions

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Study anywhere. Anytime. Across all devices.

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