Chapter 5: Q. 5.39 (page 513)

Simplify each expression:
$ⓐ {(\frac{p}{10})}^{4} ⓑ {(\frac{m}{n})}^{- 7} ⓒ {(\frac{3 a b^{3}}{c^{2}})}^{4} ⓓ {(\frac{3 x}{- 2 y^{3}})}^{3}$

Short Answer

Expert verified

The simplified expression of ${(\frac{p}{10})}^{4} = \frac{p^{4}}{10000}$

The simplified expression of ${(\frac{m}{n})}^{- 7} = \frac{n^{7}}{m^{7}}$

The simplified expression of ${(\frac{3 a b^{3}}{c^{2}})}^{4} = \frac{81 a^{4} b^{12}}{c^{8}}$

The simplified expression of ${(\frac{3 x}{- 2 y^{3}})}^{3} = \frac{27 x^{3}}{- 8 y^{9}}$

Step by step solution

Step 1. Given Information

In the given question we have to simplify each expression:

$ⓐ {(\frac{p}{10})}^{4} ⓑ {(\frac{m}{n})}^{- 7} ⓒ {(\frac{3 a b^{3}}{c^{2}})}^{4} ⓓ {(\frac{3 x}{- 2 y^{3}})}^{3}$

Part (a) Step 1. The given expression is p104

Use Quotient to a Power Property, ${(\frac{a}{b})}^{m} = \frac{a^{m}}{b^{m}}$

${(\frac{p}{10})}^{4} = \frac{p^{4}}{10^{4}}$

Simplify.

${(\frac{p}{10})}^{4} = \frac{p^{4}}{10000}$

Part (b) Step 1. The given expression is mn−7

Raise the numerator and denominator to the power.

${(\frac{m}{n})}^{- 7} = \frac{m^{- 7}}{n^{- 7}}$

Use the definition of negative exponent.

${(\frac{m}{n})}^{- 7} = \frac{1}{m^{7}} \cdot \frac{n^{7}}{1}$

Multiply.

${(\frac{m}{n})}^{- 7} = \frac{n^{7}}{m^{7}}$

Part (c) Step 1. The given expression is 3ab3c24

Use Quotient to a Power Property, ${(\frac{a}{b})}^{m} = \frac{a^{m}}{b^{m}}$

${(\frac{3 a b^{3}}{c^{2}})}^{4} = \frac{{(3)}^{4} {(a)}^{4} {(b^{3})}^{4}}{{(c^{2})}^{4}}$

Use the Product to a Power Property, ${(a b)}^{m} = a^{m} b^{m}$

${(\frac{3 a b^{3}}{c^{2}})}^{4} = \frac{81 a^{4} (b^{3 \cdot 4})}{(c^{2 \cdot 4})}$

${(\frac{3 a b^{3}}{c^{2}})}^{4} = \frac{81 a^{4} b^{12}}{c^{8}}$

Part (d) Step 1. The given expression is 3x−2y33

Use Quotient to a Power Property, ${(\frac{a}{b})}^{m} = \frac{a^{m}}{b^{m}}$

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

Use the Product to a Power Property, ${(a b)}^{m} = a^{m} b^{m}$

${(\frac{3 x}{- 2 y^{3}})}^{3} = \frac{27 x^{3}}{(- 8) (y^{3 \cdot 3})}$

${(\frac{3 x}{- 2 y^{3}})}^{3} = \frac{27 x^{3}}{(- 8) (y^{9})}$

${(\frac{3 x}{- 2 y^{3}})}^{3} = \frac{27 x^{3}}{- 8 y^{9}}$

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Simplify each expression:
$ⓐ {(\frac{p}{10})}^{4} ⓑ {(\frac{m}{n})}^{- 7} ⓒ {(\frac{3 a b^{3}}{c^{2}})}^{4} ⓓ {(\frac{3 x}{- 2 y^{3}})}^{3}$

Short Answer

Step by step solution

Step 1. Given Information

Part (a) Step 1. The given expression is p104

Part (b) Step 1. The given expression is mn−7

Part (c) Step 1. The given expression is 3ab3c24

Part (d) Step 1. The given expression is 3x−2y33

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Simplify each expression:ⓐp104ⓑmn−7ⓒ3ab3c24ⓓ3x−2y33

Short Answer

Step by step solution

Step 1. Given Information

Part (a) Step 1. The given expression is p104

Part (b) Step 1. The given expression is mn−7

Part (c) Step 1. The given expression is 3ab3c24

Part (d) Step 1. The given expression is 3x−2y33

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Logic and Functions

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Theoretical and Mathematical Physics

Mechanics Maths

Decision Maths

Study anywhere. Anytime. Across all devices.

Simplify each expression:
$ⓐ {(\frac{p}{10})}^{4} ⓑ {(\frac{m}{n})}^{- 7} ⓒ {(\frac{3 a b^{3}}{c^{2}})}^{4} ⓓ {(\frac{3 x}{- 2 y^{3}})}^{3}$