Chapter 5: Q. 123. (page 521)

In the following exercises, simplify each expression using the quotient to a power property.
(a) ${(\frac{p}{2})}^{5}$
(b) ${(\frac{x}{y})}^{- 6}$
(c) ${(\frac{2 x y^{2}}{z})}^{3}$
(d) ${(\frac{4 p^{- 3}}{q^{2}})}^{2}$

Short Answer

Expert verified

(a) $(\frac{p^{5}}{32})$

(b) $\frac{y^{6}}{x^{6}}$

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

Step by step solution

Part (a) Step 1. Given information.

The given information is (p/2)⁵.

Part (a) Step 2. Calculate the expression.

Calculate the expression by power product.

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

So,

${(\frac{p}{2})}^{5} = \frac{p^{5}}{32} .$

Part (b) Step 1. Given information.

The given expression is ${(\frac{x}{y})}^{- 6}$ .

Part (b) Step 2. Calculate the expression.

Calculate the expression by negative exponent.

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

So,

${(\frac{x}{y})}^{- 6} = \frac{y^{6}}{x^{6}}$

Part (c) Step 1. Given information.

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

Part (c) Step 2. Calculate the expression.

Calculate by applying the power product rule.

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

Part (d) Step 1. Given information.

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

Part (d) Step 2. Calculate the expression.

Calculate the expression by applying power product.

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

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In the following exercises, simplify each expression using the quotient to a power property.
(a) ${(\frac{p}{2})}^{5}$
(b) ${(\frac{x}{y})}^{- 6}$
(c) ${(\frac{2 x y^{2}}{z})}^{3}$
(d) ${(\frac{4 p^{- 3}}{q^{2}})}^{2}$

Short Answer

Step by step solution

Part (a) Step 1. Given information.

Part (a) Step 2. Calculate the expression.

Part (b) Step 1. Given information.

Part (b) Step 2. Calculate the expression.

Part (c) Step 1. Given information.

Part (c) Step 2. Calculate the expression.

Part (d) Step 1. Given information.

Part (d) Step 2. Calculate the expression.

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In the following exercises, simplify each expression using the quotient to a power property.(a) p25(b) xy-6(c) 2xy2z3(d)4p-3q22

Short Answer

Step by step solution

Part (a) Step 1. Given information.

Part (a) Step 2. Calculate the expression.

Part (b) Step 1. Given information.

Part (b) Step 2. Calculate the expression.

Part (c) Step 1. Given information.

Part (c) Step 2. Calculate the expression.

Part (d) Step 1. Given information.

Part (d) Step 2. Calculate the expression.

One App. One Place for Learning.

Most popular questions from this chapter

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Logic and Functions

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Study anywhere. Anytime. Across all devices.

In the following exercises, simplify each expression using the quotient to a power property.
(a) ${(\frac{p}{2})}^{5}$
(b) ${(\frac{x}{y})}^{- 6}$
(c) ${(\frac{2 x y^{2}}{z})}^{3}$
(d) ${(\frac{4 p^{- 3}}{q^{2}})}^{2}$