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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. 125. (page 521)

In the following exercises, simplify each expression using the quotient to a power property.
(a) ${(\frac{a}{3 b})}^{4}$
(b) ${(\frac{5}{4 m})}^{- 2}$
(c) ${(\frac{2 x y^{2}}{z})}^{3}$
(d) ${(\frac{4 p^{- 3}}{q^{2}})}^{2}$

Short Answer

Expert verified

(a) $\frac{a^{4}}{81 b^{4}}$

(b) $\frac{16 m^{2}}{25}$

(c) $\frac{8 x^{3} y^{6}}{z^{3}}$

(d) $\frac{16 p^{- 6}}{q^{4}}$

Step by step solution

01

Part (a) Step 1. Given information.

The given expression is ${(\frac{a}{3 b})}^{4}$ .

02

Part (a) Step 2. Calculate the expression.

Applying the concept of power product.

${(\frac{a}{b})}^{n} = \frac{a^{n}}{b^{n}}$

So,

${(\frac{a}{3 b})}^{4} = \frac{a^{4}}{81 b^{4}}$ .

03

Part (b) Step 1. Given information.

The given expression is ${(\frac{5}{4 m})}^{- 2}$ .

04

Part (b) Step 2. Calculate the expression.

Calculate the expression by applying concept of negative exponent.

So,

${(\frac{5}{4 m})}^{- 2} = \frac{16 m^{2}}{25}$

05

Part (c) Step 1. Given information.

The given expression is ${(\frac{2 x y^{2}}{z})}^{3}$ .

06

Part (c) Step 2. Calculate the expression.

Calculate the expression by applying the concept of power product.

So,

${(\frac{2 x y^{2}}{z})}^{3} = (\frac{2^{3} x^{3} y^{2 路 3}}{z^{3}}) = \frac{8 x^{3} y^{6}}{z^{3}}$

07

Part (d) Step 1. Given information.

The given expression is ${(\frac{4 p^{- 3}}{q^{2}})}^{2}$ .

08

Part (d) Step 2. Calculate the expression.

The given expression is calculated by applying the concept of power product.

So,

${(\frac{4 p^{- 3}}{q^{2}})}^{2} = \frac{16 p^{- 6}}{q^{4}}$ .

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Most popular questions from this chapter

Use synthetic division to find the quotient and remainder.

$x^{3} - 6 x^{2} + 5 x + 14$ is divided by $x + 1$

Add or subtract: $(a) - 15 c^{2} + 8 c^{2} (b) - 15 y^{2} z^{3} - (- 5 y^{2} z^{3})$

In the following exercises . Simplify the expression

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

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

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$(7 q + 4) (3 q - 8)$

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