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

Part(a)-Step 1. Given information

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

The main objective is to simplify the expression.

Part(a)-Step 2. Simplify

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

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

Part(b)-Step 1. Given information.

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

The main objective is to simplify the expression.

Part(b)-Step2. Simplify

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

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

Part(c)-Step 1. Given information

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

The main objective is to simplify the expression.

Part(c)-Step 2. Simplify

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

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

Part(d)-Step 1. Given information

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

The main objective is to simplify the expression.

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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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

Step by step solution

Part(a)-Step 1. Given information

Part(a)-Step 2. Simplify

Part(b)-Step 1. Given information.

Part(b)-Step2. Simplify

Part(c)-Step 1. Given information

Part(c)-Step 2. Simplify

Part(d)-Step 1. Given information

Part(d)-Step 2. Simplify

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In the following exercises, simplify each expression using the properties for exponents.ap21p7b41644cbb9d446

Short Answer

Step by step solution

Part(a)-Step 1. Given information

Part(a)-Step 2. Simplify

Part(b)-Step 1. Given information.

Part(b)-Step2. Simplify

Part(c)-Step 1. Given information

Part(c)-Step 2. Simplify

Part(d)-Step 1. Given information

Part(d)-Step 2. Simplify

One App. One Place for Learning.

Most popular questions from this chapter

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Study anywhere. Anytime. Across all devices.

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