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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. 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

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 ${(b^{2})}^{7}$ .

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

03

Part a Step 2. Simplify

Using the Power property of exponents.

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

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

04

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.

05

Part b Step 2. Simplify

Using the Power property for exponent,

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

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

06

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.

07

Part c Step 2. Simplify

Using the Power property for exponents

$\begin{matrix} {(k^{2})}^{鈭� 5} = k^{2 鈰� (鈭� 5)} \\ = k^{鈭� 10} \end{matrix}$

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

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Most popular questions from this chapter

In the following exercises, find product of ${(a^{5} 鈥� 鈭� 鈥� 7 b)}^{2}$ .

In the following exercises, find the product of $(x^{2} 鈥� + 鈥� 8 y) (8 x 鈥� 鈭� 鈥� y^{2})$ .

Multiply each pair of conjugates using the product of the conjugates pattern.

$(m + \frac{2}{3} n) (m - \frac{2}{3} n)$

$Add: (a) 8 y^{2} + 3 z^{2} - 3 y^{2} (b) m^{2} n^{2} - 8 m^{2} + 4 n^{2} .$

Multiply each pair of conjugates using the product of the conjugates pattern.

$(a b - 4) (a b + 4)$

See all solutions

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