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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. 115 (page 521)

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

Short Answer

Expert verified

The simplified expression are:

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

Step by step solution

01

Step 1. Power property for exponents

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

${(a^{m})}^{n} = a^{m 路 n}$

02

Part a Step 1. Given information

The given expression is ${(m^{4})}^{2}$ .

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

03

Part a Step 2. Simplify

Using Power property for exponents,

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

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

04

Part b Step 1. Given information

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

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

05

Part b Step 2. Simplify

Using Power property for exponents,

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

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

06

Part c Step 1. Given information

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

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

07

Part c Step 2. Simplify

Using Power property for exponents,

$\begin{matrix} {(x^{3})}^{鈭� 4} = x^{3 鈰� (鈭� 4)} \\ = x^{鈭� 12} \end{matrix}$

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

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Most popular questions from this chapter

In the following exercises, multiply the binomials. Use any method.

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