Chapter 8: Q. 8.95 (page 803)

Simplify:
(a) $\frac{\sqrt{162 x^{10} y^{2}}}{\sqrt{2 x^{6} y^{6}}}$
(b) $\frac{\sqrt[3]{128 x^{2} y^{- 1}}}{\sqrt[3]{2 x^{- 1} y^{2}}}$

Short Answer

Expert verified

The simplification of $\frac{\sqrt{162 x^{10} y^{2}}}{\sqrt{2 x^{6} y^{6}}}$ is $\frac{9 x^{2}}{y^{2}}$

The simplification of $\frac{\sqrt[3]{128 x^{2} y^{- 1}}}{\sqrt[3]{2 x^{- 1} y^{2}}}$ is $\frac{4 x}{y}$

Step by step solution

Part (a) Step 1. Given

An expression $\frac{\sqrt{162 x^{10} y^{2}}}{\sqrt{2 x^{6} y^{6}}}$

To simplify the expression

Part (a) Step 2. Rewrite using the quotient property

Rewrite using the quotient property

$\frac{\sqrt{162 x^{10} y^{2}}}{\sqrt{2 x^{6} y^{6}}} = \sqrt{\frac{162 x^{10} y^{2}}{2 x^{6} y^{6}}}$

Remove the common factors.

$= \sqrt{\frac{81 x^{4}}{y^{4}}}$

Part (a) Step 3. Simplify the expression

$\frac{\sqrt{162 x^{10} y^{2}}}{\sqrt{2 x^{6} y^{6}}} = \sqrt{\frac{81 x^{4}}{y^{4}}}$

$= \sqrt{\frac{9^{2} {(x^{2})}^{2}}{{(y^{2})}^{2}}}$

$= \frac{9 x^{2}}{y^{2}}$

The simplification of the expression is $\frac{9 x^{2}}{y^{2}}$

Part (b) Step 1. Given

An expression $\frac{\sqrt[3]{128 x^{2} y^{- 1}}}{\sqrt[3]{2 x^{- 1} y^{2}}}$

To simplify the expression

Part (b) Step 2. Rewrite using the quotient property

Rewrite using the quotient property

$\frac{\sqrt[3]{128 x^{2} y^{- 1}}}{\sqrt[3]{2 x^{- 1} y^{2}}} = \sqrt[3]{\frac{128 x^{2} y^{- 1}}{2 x^{- 1} y^{2}}}$

Remove the common factors.

$= \sqrt[3]{\frac{64 x^{3}}{y^{3}}}$

Part (b) Step 3. Simplify the expression

$\frac{\sqrt[3]{128 x^{2} y^{- 1}}}{\sqrt[3]{2 x^{- 1} y^{2}}} = \sqrt[3]{\frac{64 x^{3}}{y^{3}}}$

$= \sqrt[3]{\frac{4^{3} x^{3}}{y^{3}}}$

$= \frac{4 x}{y}$

The simplification of the expression is $\frac{4 x}{y}$

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Simplify:
(a) $\frac{\sqrt{162 x^{10} y^{2}}}{\sqrt{2 x^{6} y^{6}}}$
(b) $\frac{\sqrt[3]{128 x^{2} y^{- 1}}}{\sqrt[3]{2 x^{- 1} y^{2}}}$

Short Answer

Step by step solution

Part (a) Step 1. Given

Part (a) Step 2. Rewrite using the quotient property

Part (a) Step 3. Simplify the expression

Part (b) Step 1. Given

Part (b) Step 2. Rewrite using the quotient property

Part (b) Step 3. Simplify the expression

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Simplify:(a)162x10y22x6y6(b) 128x2y-132x-1y23

Short Answer

Step by step solution

Part (a) Step 1. Given

Part (a) Step 2. Rewrite using the quotient property

Part (a) Step 3. Simplify the expression

Part (b) Step 1. Given

Part (b) Step 2. Rewrite using the quotient property

Part (b) Step 3. Simplify the expression

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Theoretical and Mathematical Physics

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Decision Maths

Study anywhere. Anytime. Across all devices.

Simplify:
(a) $\frac{\sqrt{162 x^{10} y^{2}}}{\sqrt{2 x^{6} y^{6}}}$
(b) $\frac{\sqrt[3]{128 x^{2} y^{- 1}}}{\sqrt[3]{2 x^{- 1} y^{2}}}$