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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.91 (page 520)

In the following exercises, simplify each expression using the properties for exponents.
$(a) \frac{p^{21}}{p^{7}} (b) \frac{4^{16}}{4^{4}} (c) \frac{b}{b^{9}} (d) \frac{4}{4^{6}}$

Short Answer

Expert verified

The simplified form is:

$\begin{array}{rcl} (a) \frac{p^{21}}{p^{7}} & = & p^{14} \\ (b) \frac{4^{16}}{4^{4}} & = & 4^{12} \\ (c) \frac{b}{b^{9}} & = & \frac{1}{b^{8}} \\ (d) \frac{4}{4^{6}} & = & \frac{1}{4^{5}} \end{array}$

Step by step solution

01

Part(a)-Step 1. Given information

The given information is $\frac{p^{21}}{p^{7}}$ .

The main objective is to simplify the expression.

02

Part(a)-Step 2. Simplify

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

$\begin{array}{rcl} \frac{p^{21}}{p^{7}} & = & p^{21 - 7} \\ = & p^{14} \end{array}$ .

03

Part(b)-Step 1. Given information.

The given information is $\frac{4^{16}}{4^{4}}$ .

The main objective is to simplify the expression.

04

Part(b)-Step2. Simplify

Use the property that $\frac{a^{m}}{a^{n}} = a^{m - n}, m > n$ .

$\begin{array}{rcl} \frac{4^{16}}{4^{4}} & = & 4^{16 - 4} \\ = & 4^{12} \end{array}$

05

Part(c)-Step 1. Given information

The given information is $\frac{b}{b^{9}}$ .

The main objective is to simplify the expression.

06

Part(c)-Step 2. Simplify

Use the property that $\frac{a^{m}}{a^{n}} = \frac{1}{a^{n - m}}, n > m$ .

$\begin{array}{rcl} \frac{b}{b^{9}} & = & \frac{1}{b^{9 - 1}} \\ = & \frac{1}{b^{8}} \end{array}$

07

Part(d)-Step 1. Given information

The given information is $\frac{4}{4^{6}}$ .

The main objective is to simplify the expression.

08

Part(d)-Step 2. Simplify

Use the property that $\frac{a^{m}}{a^{n}} = \frac{1}{a^{n - m}}, n > m$ .

$\begin{array}{rcl} \frac{4}{4^{6}} & = & \frac{4^{1}}{4^{6}} \\ = & \frac{1}{4^{6 - 1}} \\ = & \frac{1}{4^{5}} \end{array}$

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Most popular questions from this chapter

Use synthetic division to find the quotient and remainder.

$x^{3} - 6 x^{2} + 5 x + 14$ is divided by $x + 1$

Multiply each pair of conjugates using the product of the conjugates pattern.

$(5 k + 6) (5 k - 6)$

Multiply each pair of conjugates using the product of the conjugates pattern.

$(m + \frac{2}{3} n) (m - \frac{2}{3} n)$

Simplify ${(4 x^{3})}^{3} {(2 x^{5})}^{4}$

Multiply each pair of conjugates using the product of the conjugates pattern.

$(11 k + 4) (11 k - 4)$

See all solutions

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