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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. 124. (page 521)

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

Short Answer

Expert verified

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

(b) $\frac{b^{5}}{a^{5}}$

(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 ${(\frac{x}{3})}^{4}$ .

02

Part (a) Step 2. Calculate the expression.

Calculate the expression by applying power product.

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

So,

${(\frac{x}{3})}^{4} = \frac{x^{4}}{81}$

03

Part (b) Step 1. Given information.

The given expression is ${(\frac{a}{b})}^{- 5} .$

04

Part (b) Step 2. Calculate the expression.

Calculate the expression by applying the negative exponent.

${(\frac{a}{b})}^{- 5} = \frac{b^{5}}{a^{5}}$ .

05

Part (c) Step 1. Given expression.

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 power product.

So,

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

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.

Apply the concept of power product to the expression.

So,

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

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Most popular questions from this chapter

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

$(x + 8) (x + 3)$

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

$(p + \frac{4}{5} q) (p - \frac{4}{5} q)$

Multiply : (a) (-6b⁴)(-9b⁵)

(b) $(\frac{2}{3} r^{5} s) (12 r^{6} s^{7})$

Write number (a) 340,000 (b) 0.041 in scientific notation

Simplify ${(4 x^{3})}^{3} {(2 x^{5})}^{4}$

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