Chapter 8: Q. 586. (page 857)

In the following exercises, simplify. Assume all variables are positive.
${(\frac{8 x^{\frac{2}{3}} y^{- \frac{5}{2}}}{x^{- \frac{7}{3}} y^{\frac{1}{2}}})}^{\frac{1}{3}}$

Short Answer

Expert verified

The simplified form of the given expression is $\frac{2 x}{y}$ .

Step by step solution

Step 1. Given information.

The given expression is ${(\frac{8 x^{\frac{2}{3}} y^{- \frac{5}{2}}}{x^{- \frac{7}{3}} y^{\frac{1}{2}}})}^{\frac{1}{3}}$

Step 2. Simplify the exponents.

Applying the Negative Exponent Property,

${(\frac{8 x^{\frac{2}{3}} y^{- \frac{5}{2}}}{x^{- \frac{7}{3}} y^{\frac{1}{2}}})}^{\frac{1}{3}} = {(\frac{8 x^{\frac{2}{3}} x^{\frac{7}{3}}}{y^{\frac{5}{2}} y^{\frac{1}{2}}})}^{\frac{1}{3}}$

Now we will use the Product property,

${(\frac{8 x^{\frac{2}{3} + \frac{7}{3}}}{y^{\frac{5}{2} + \frac{1}{2}}})}^{\frac{1}{3}} = {(\frac{8 x^{\frac{9}{3}}}{y^{\frac{6}{2}}})}^{\frac{1}{3}} = {(\frac{8 x^{3}}{y^{3}})}^{\frac{1}{3}}$

Let's use the Power Property,

$(\frac{8^{\frac{1}{3}} x^{3 \cdot \frac{1}{3}}}{y^{3 \cdot \frac{1}{3}}}) = \frac{2 x}{y}$

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In the following exercises, simplify. Assume all variables are positive.
${(\frac{8 x^{\frac{2}{3}} y^{- \frac{5}{2}}}{x^{- \frac{7}{3}} y^{\frac{1}{2}}})}^{\frac{1}{3}}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the exponents.

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In the following exercises, simplify. Assume all variables are positive.8x23y-52x-73y1213

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the exponents.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Theoretical and Mathematical Physics

Decision Maths

Geometry

Calculus

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises, simplify. Assume all variables are positive.
${(\frac{8 x^{\frac{2}{3}} y^{- \frac{5}{2}}}{x^{- \frac{7}{3}} y^{\frac{1}{2}}})}^{\frac{1}{3}}$