Chapter 5: Q. 126. (page 521)

In the following exercises, simplify each expression using the quotient to a power property.
(a) ${(\frac{x}{2 y})}^{3}$
(b) ${(\frac{10}{3 q})}^{- 4}$
(c) ${(\frac{2 x y^{2}}{z})}^{3}$
(d) ${(\frac{4 p^{- 3}}{q^{2}})}^{2}$

Short Answer

Expert verified

(a) $\frac{x^{3}}{8 y^{3}}$

(b) $\frac{81 q^{4}}{10^{4}}$

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

Step by step solution

Part (a) Step 1. Given information.

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

Part (a) Step 2. Calculate the expression.

To calculate the expression apply the concept of power product.

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

So,

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

Part (b) Step 1. Given information.

The given expression is ${(\frac{10}{3 q})}^{- 4}$ .

Part (b) Step 2. Calculate the expression.

Apply the concept of negative exponent to the expression.

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

So,

${(\frac{10}{3 q})}^{- 4} = {(\frac{3 q}{10})}^{4}$

Now apply the power product rule.

${(\frac{3 q}{10})}^{4} = \frac{81 q^{4}}{10^{4}}$

Part (c) Step 1. Given information.

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

Part (c) Step 2. Calculate the expression.

Apply the concept of power product.

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

Part (d) Step 1. Given information.

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

Part (d) Step 2. Calculate the expression.

To calculate the expression apply the concept of power rule.

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

So,

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

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In the following exercises, simplify each expression using the quotient to a power property.
(a) ${(\frac{x}{2 y})}^{3}$
(b) ${(\frac{10}{3 q})}^{- 4}$
(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) x2y3(b) 103q-4(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.

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In the following exercises, simplify each expression using the quotient to a power property.
(a) ${(\frac{x}{2 y})}^{3}$
(b) ${(\frac{10}{3 q})}^{- 4}$
(c) ${(\frac{2 x y^{2}}{z})}^{3}$
(d) ${(\frac{4 p^{- 3}}{q^{2}})}^{2}$