Chapter 5: Q. 116 (page 521)

In the following exercises, simplify each expression using the Power Property.
$(a) {(b^{2})}^{7} (b) {(3^{8})}^{2} (c) {(k^{2})}^{- 5}$

Short Answer

Expert verified

The simplified expression are:

$(a) {(b^{2})}^{7} = b^{14} (b) {(3^{8})}^{2} = 3^{16} (c) {(k^{2})}^{- 5} = k^{- 10}$

Step by step solution

Step 1. Power property for exponents

If a is a real number and m and n are integers, then

${(a^{m})}^{n} = a^{m \cdot n}$

Part a Step 1. Given information

The given expression is ${(b^{2})}^{7}$ .

We have to simplify the given expression using Power property for exponent.

Part a Step 2. Simplify

Using the Power property of exponents.

$\begin{matrix} {(b^{2})}^{7} = b^{2 \cdot 7} \\ = b^{14} \end{matrix}$

So, the simplified expression is ${(b^{2})}^{7} = b^{14}$

Part b Step 1. Given information

The given expression is ${(3^{8})}^{2}$ .

We have to simplify the given expression using Power property for exponent.

Part b Step 2. Simplify

Using the Power property for exponent,

$\begin{matrix} {(3^{8})}^{2} = 3^{8 \cdot 2} \\ = 3^{16} \end{matrix}$

So, the simplified expression is ${(3^{8})}^{2} = 3^{16}$

Part c Step 1. Given information

The given expression is ${(k^{2})}^{- 5}$ .

We have to simplify the given expression using Power property for exponent.

Part c Step 2. Simplify

Using the Power property for exponents

$\begin{matrix} {(k^{2})}^{- 5} = k^{2 \cdot (- 5)} \\ = k^{- 10} \end{matrix}$

So, the simplified the expression is ${(k^{2})}^{- 5} = k^{- 10}$

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In the following exercises, simplify each expression using the Power Property.
$(a) {(b^{2})}^{7} (b) {(3^{8})}^{2} (c) {(k^{2})}^{- 5}$

Short Answer

Step by step solution

Step 1. Power property for exponents

Part a Step 1. Given information

Part a Step 2. Simplify

Part b Step 1. Given information

Part b Step 2. Simplify

Part c Step 1. Given information

Part c Step 2. Simplify

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In the following exercises, simplify each expression using the Power Property.ab27b382ck2-5

Short Answer

Step by step solution

Step 1. Power property for exponents

Part a Step 1. Given information

Part a Step 2. Simplify

Part b Step 1. Given information

Part b Step 2. Simplify

Part c Step 1. Given information

Part c Step 2. Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Logic and Functions

Geometry

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Pure Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, simplify each expression using the Power Property.
$(a) {(b^{2})}^{7} (b) {(3^{8})}^{2} (c) {(k^{2})}^{- 5}$