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

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

Step by step solution

Part (a) Step 1. Given information.

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

Part (a) Step 2. Calculate the expression.

Calculate the expression by applying power product.

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

So,

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

Part (b) Step 1. Given information.

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

Part (b) Step 2. Calculate the expression.

Calculate the expression by applying the negative exponent.

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

Part (c) Step 1. Given expression.

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

Part (c) Step 2. Calculate the expression.

Calculate the expression by applying the power product.

So,

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

Part (d) Step 1. Given information.

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

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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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

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 expression.

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) x34(b) ab-5(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 expression.

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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Decision Maths

Statistics

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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) ${(\frac{x}{3})}^{4}$
(b) ${(\frac{a}{b})}^{- 5}$
(c) ${(\frac{2 x y^{2}}{z})}^{3}$
(d) ${(\frac{4 p^{- 3}}{q^{2}})}^{2}$