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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. 118 (page 521)

In the following exercises, simplify each expression using the Power Property.
$(a) {(x^{2})}^{y} (b) {(7^{a})}^{b} (c) {(a^{9})}^{- 10}$

Short Answer

Expert verified

The simplified expression are:

$(a) {(x^{2})}^{y} = x^{2 y} (b) {(7^{a})}^{b} = 7^{a b} (c) {(a^{9})}^{- 10} = a^{- 90}$

Step by step solution

01

Step 1. Power properties 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 ${(x^{2})}^{y}$ .

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

03

Part a Step 2. Simplify

Using Power property for exponent,

$\begin{matrix} {(x^{2})}^{y} = x^{2 鈰� y} \\ = x^{2 y} \end{matrix}$

So, the simplified expression is ${(x^{2})}^{y} = x^{2 y}$

04

Part b Step 1. Given information

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

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

05

Part b Step 2. Simplify

Using the Power property for exponents,

$\begin{matrix} {(7^{a})}^{b} = 7^{a 鈰� b} \\ = 7^{a b} \end{matrix}$

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

06

Part c Step 1. Given information

The given expression is ${(a^{9})}^{- 10}$ .

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

07

Part c Step 2. Simplify

Using Power properties for exponent,

$\begin{matrix} {(a^{9})}^{鈭� 10} = a^{9 鈰� (鈭� 10)} \\ = a^{鈭� 90} \end{matrix}$

So, the simplified expression is ${(a^{9})}^{- 10} = a^{- 90}$

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Most popular questions from this chapter

Multiply (a) $(3 脳 10^{- 5}) (3 脳 10^{9})$ to get answer in decimal form

Divide (b) $\frac{7 脳 10^{- 3}}{1 脳 10^{- 7}}$ to get answer in decimal form

Simplify

(a) ${(2 r^{- 2})}^{3} {(4^{- 1} r)}^{2}$ (b) ${(3 x^{- 3})}^{3} {(3^{- 1} x^{5})}^{4}$

Solve the square using the binomial squares pattern.

${(y + \frac{1}{4})}^{2}$

Use the Product Property for Exponents to explain $x 路 x = x^{2}$

Write number (a) 1,290,000 (b) 0.00000103 in scientific notation

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