Chapter 6: Q. 132 (page 711)

In the following exercises, simplify each expression.
$ⓐ {(m^{2} n)}^{2} {(2 m n^{5})}^{4} ⓑ {(3 p q^{4})}^{2} {(6 p^{6} q)}^{2}$

Short Answer

Expert verified

(a) The simplified form of the given expression is $16 m^{8} n^{22}$ .

(b) The simplified form of the given expression is ${324 p^{14} q}^{10}$ .

Step by step solution

Step 1. Given Information

In the following exercises, we have to simplify given expression.
$ⓐ {(m^{2} n)}^{2} {(2 m n^{5})}^{4} ⓑ {(3 p q^{4})}^{2} {(6 p^{6} q)}^{2}$

Part (a) Step 1. Given expression is (m2n)2(2mn5)4

Use the Power Property.

${(m^{2} n)}^{2} {(2 m n^{5})}^{4} = {{(m^{2})}^{2} \cdot (n)}^{2} {\cdot {(2)}^{4} \cdot {(m)}^{4} \cdot (n^{5})}^{4} {(m^{2} n)}^{2} {(2 m n^{5})}^{4} = m^{2 \cdot 2} \cdot n^{2} \cdot 16 \cdot m^{4} \cdot n^{5 \cdot 4} {(m^{2} n)}^{2} {(2 m n^{5})}^{4} = m^{4} \cdot n^{2} \cdot 16 \cdot m^{4} \cdot n^{20}$

Add the exponents.

${(m^{2} n)}^{2} {(2 m n^{5})}^{4} = 16 \cdot m^{4 + 4} \cdot n^{20 + 2} {(m^{2} n)}^{2} {(2 m n^{5})}^{4} = 16 m^{8} n^{22}$

Part (b) Step 1. Given expression is (3pq4)2(6p6q)2

Use the Power Property.

${(3 p q^{4})}^{2} {(6 p^{6} q)}^{2} {= {(3)}^{2} \cdot {(p)}^{2} \cdot (q^{4})}^{2} {\cdot {(6)}^{2} \cdot {(p^{6})}^{2} \cdot (q)}^{2} {(3 p q^{4})}^{2} {(6 p^{6} q)}^{2} = 9 \cdot p^{2} \cdot q^{4 \cdot 2} {\cdot 36 \cdot p^{6 \cdot 2} \cdot q}^{2} {(3 p q^{4})}^{2} {(6 p^{6} q)}^{2} = 9 \cdot p^{2} \cdot q^{8} {\cdot 36 \cdot p^{12} \cdot q}^{2}$

Add the exponents.

${(3 p q^{4})}^{2} {(6 p^{6} q)}^{2} = 9 {\cdot 36 \cdot p^{12 + 2} \cdot q}^{2 + 8} {(3 p q^{4})}^{2} {(6 p^{6} q)}^{2} = {324 p^{14} q}^{10}$

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In the following exercises, simplify each expression.
$ⓐ {(m^{2} n)}^{2} {(2 m n^{5})}^{4} ⓑ {(3 p q^{4})}^{2} {(6 p^{6} q)}^{2}$

Short Answer

Step by step solution

Step 1. Given Information

Part (a) Step 1. Given expression is (m2n)2(2mn5)4

Part (b) Step 1. Given expression is (3pq4)2(6p6q)2

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In the following exercises, simplify each expression.ⓐ(m2n)2(2mn5)4ⓑ(3pq4)2(6p6q)2

Short Answer

Step by step solution

Step 1. Given Information

Part (a) Step 1. Given expression is (m2n)2(2mn5)4

Part (b) Step 1. Given expression is (3pq4)2(6p6q)2

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Study anywhere. Anytime. Across all devices.

In the following exercises, simplify each expression.
$ⓐ {(m^{2} n)}^{2} {(2 m n^{5})}^{4} ⓑ {(3 p q^{4})}^{2} {(6 p^{6} q)}^{2}$