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

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

Step by step solution

Part (a) Step 1. Given information.

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

Part (a) Step 2. Calculate the expression.

Applying the concept of power product.

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

So,

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

Part (b) Step 1. Given information.

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

Part (b) Step 2. Calculate the expression.

Calculate the expression by applying concept of negative exponent.

So,

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

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 the expression by applying the concept of power product.

So,

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

Part (d) Step 1. Given information.

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

Part (d) Step 2. Calculate the expression.

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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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

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)a3b4(b) 54m-2(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.

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