Chapter 5: Q. 115 (page 521)

In the following exercises, simplify each expression using the Power Property.
$\begin{array}{l} (a) {(m^{4})}^{2} \\ (b) {(10^{3})}^{6} \\ (c) {(x^{3})}^{- 4} \end{array}$

Short Answer

Expert verified

The simplified expression are:

$\begin{array}{l} (a) {(m^{4})}^{2} = m^{8} \\ (b) {(10^{3})}^{6} = 10^{18} \\ (c) {(x^{3})}^{- 4} = x^{- 12} \end{array}$

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 ${(m^{4})}^{2}$ .

We have to simplify the expression using Power property for exponents.

Part a Step 2. Simplify

Using Power property for exponents,

\begin{matrix} {(m^{4})}^{2} = m^{4 \cdot 2} \\ = m^{8} \end{matrix}

So, The simplified expression is ${(m^{4})}^{2} = m^{8}$

Part b Step 1. Given information

The given expression is ${(10^{3})}^{6}$

We have to simplify the expression using Power property for exponents.

Part b Step 2. Simplify

Using Power property for exponents,

$\begin{matrix} {(10^{3})}^{6} = 10^{3 \cdot 6} \\ = 10^{18} \end{matrix}$

So, the simplified expression is ${(10^{3})}^{6} = 10^{18}$

Part c Step 1. Given information

The given expression is ${(x^{3})}^{- 4}$ .

We have to simplify the expression using Power property for exponents.

Part c Step 2. Simplify

Using Power property for exponents,

$\begin{matrix} {(x^{3})}^{- 4} = x^{3 \cdot (- 4)} \\ = x^{- 12} \end{matrix}$

So, the simplified expression is ${(x^{3})}^{- 4} = x^{- 12}$

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In the following exercises, simplify each expression using the Power Property.
$\begin{array}{l} (a) {(m^{4})}^{2} \\ (b) {(10^{3})}^{6} \\ (c) {(x^{3})}^{- 4} \end{array}$

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.am42b1036cx3−4

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

Geometry

Decision Maths

Applied Mathematics

Logic and Functions

Statistics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In the following exercises, simplify each expression using the Power Property.
$\begin{array}{l} (a) {(m^{4})}^{2} \\ (b) {(10^{3})}^{6} \\ (c) {(x^{3})}^{- 4} \end{array}$