Chapter 6: Q. 130 (page 711)

In the following exercises, simplify each expression.
$ⓐ {(\frac{2}{5} x^{2} y)}^{3} ⓑ {(\frac{8}{9} x y^{4})}^{2}$

Short Answer

Expert verified

(a) The simplified form of the given expression is $\frac{8}{125} x^{6} y^{3}$ .

(b) The simplified form of the given expression is $\frac{64}{81} x^{2} y^{8}$ .

Step by step solution

Step 1. Given Information

In the following exercises, we have to simplify given expression.
$ⓐ {(\frac{2}{5} x^{2} y)}^{3} ⓑ {(\frac{8}{9} x y^{4})}^{2}$

Part (a) Step 1. Given expression is 25x2y3

Use the Power Property.

${(\frac{2}{5} x^{2} y)}^{3} = {(\frac{2}{5})}^{3} \cdot {(x^{2})}^{3} \cdot y^{3} {(\frac{2}{5} x^{2} y)}^{3} = \frac{8}{125} \cdot x^{2 \cdot 3} \cdot y^{3} {(\frac{2}{5} x^{2} y)}^{3} = \frac{8}{125} x^{6} y^{3}$

Part (b) Step 1. Given expression is 89xy42

Use the Power Property.

${(\frac{8}{9} x y^{4})}^{2} = {(\frac{8}{9})}^{2} \cdot x^{2} \cdot {(y^{4})}^{2} {(\frac{8}{9} x y^{4})}^{2} = \frac{64}{81} \cdot x^{2} \cdot (y^{4 \cdot 2}) {(\frac{8}{9} x y^{4})}^{2} = \frac{64}{81} x^{2} y^{8}$

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In the following exercises, simplify each expression.
$ⓐ {(\frac{2}{5} x^{2} y)}^{3} ⓑ {(\frac{8}{9} x y^{4})}^{2}$

Short Answer

Step by step solution

Step 1. Given Information

Part (a) Step 1. Given expression is 25x2y3

Part (b) Step 1. Given expression is 89xy42

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In the following exercises, simplify each expression.ⓐ25x2y3ⓑ89xy42

Short Answer

Step by step solution

Step 1. Given Information

Part (a) Step 1. Given expression is 25x2y3

Part (b) Step 1. Given expression is 89xy42

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Pure Maths

Calculus

Statistics

Probability and Statistics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, simplify each expression.
$ⓐ {(\frac{2}{5} x^{2} y)}^{3} ⓑ {(\frac{8}{9} x y^{4})}^{2}$