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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 117. (page 521)

In the following exercises, simplify each expression using the Power Property
$(a) {(y^{3})}^{x} (b) {(5^{x})}^{y} (c) {(q^{6})}^{- 8}$

Short Answer

Expert verified

The simplified expressions are:

$(a) {(y^{3})}^{x} = y^{3 x} (b) {(5^{x})}^{y} = 5^{x y} (c) {(q^{6})}^{- 8} = q^{- 48}$

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 ${(y^{3})}^{x}$ .

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

03

Part a Step 2. Simplify

Using the Power property for exponent,

$\begin{matrix} {(y^{3})}^{x} = y^{3 鈰� x} \\ = y^{3 x} \end{matrix}$

So, the simplified expression is ${(y^{3})}^{x} = y^{3 x}$

04

Part b Step 1. Given information

The given expression is ${(5^{x})}^{y}$ .

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

05

Part b Step 2. Simplify

Using the Product power for exponent,

$\begin{matrix} {(5^{x})}^{y} = 5^{x 鈰� y} \\ = 5^{x y} \end{matrix}$

So, the simplified expression is ${(5^{x})}^{y} = 5^{x y}$

06

Part c Step 1. Given information

The given expression is ${(q^{6})}^{- 8}$ .

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

07

Part c Step 2. Simplify

Using the Power property for exponent,

$\begin{matrix} {(q^{6})}^{鈭� 8} = q^{6 鈰� (鈭� 8)} \\ = q^{鈭� 48} \end{matrix}$

So, the simplified expression is ${(q^{6})}^{- 8} = q^{- 48}$

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