Chapter 11: Q11. (page 699)

Simplify the given expression. State the excluded values of the variables.
$\frac{16 x^{2} y^{3}}{8 x y}$

Short Answer

Expert verified

The simplified expression is $2 x y^{2}$ .

The excluded values are $x = 0, y = 0$ .

Step by step solution

Step 1. Define a rational function.

A function of the form $y = \frac{p}{q}$ is called a rational function, where $p$ and $q$ are the polynomials and $q \neq 0$ .

Step 2. Define quotient of power rule.

The quotient of power rule is given by

$\frac{a^{m}}{a^{n}} = a^{m - n}$

Where, $a$ is any non-zero real number.

Step 3. Define the excluded values for the rational function.

Any value of a variable that results in a denominator of zero in a rational function is excluded from the domain of the function and these values are called the excluded values of the rational function.

Step 4. Simplify the expression 16x2y38xy.

Use quotient of power rule to simplify the expression $\frac{16 x^{2} y^{3}}{8 x y}$ .

$\begin{array}{l} \frac{16 x^{2} y^{3}}{8 x y} = (\frac{16}{8}) (\frac{x^{2}}{x}) (\frac{y^{3}}{y}) \\ = (2) (x^{2 - 1}) (y^{3 - 1}) \\ = (2) (x^{1}) (y^{2}) \\ = 2 x y^{2} \end{array}$

Step 5. State the excluded values of the variables for the expression 16x2y38xy.

For excluded value,

Denominator $= 0$

$\begin{array}{l} 8 x y = 0 \\ x y = \frac{0}{8} \\ x y = 0 \\ x = 0, y = 0 \end{array}$

Therefore,

The simplified expression is $2 x y^{2}$ .

The excluded values are $x = 0, y = 0$ .

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Simplify the given expression. State the excluded values of the variables.
$\frac{16 x^{2} y^{3}}{8 x y}$

Short Answer

Step by step solution

Step 1. Define a rational function.

Step 2. Define quotient of power rule.

Step 3. Define the excluded values for the rational function.

Step 4. Simplify the expression 16x2y38xy.

Step 5. State the excluded values of the variables for the expression 16x2y38xy.

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$x$	1	2	5
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Simplify the given expression. State the excluded values of the variables.16x2y38xy

Short Answer

Step by step solution

Step 1. Define a rational function.

Step 2. Define quotient of power rule.

Step 3. Define the excluded values for the rational function.

Step 4. Simplify the expression 16x2y38xy.

Step 5. State the excluded values of the variables for the expression 16x2y38xy.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Pure Maths

Discrete Mathematics

Decision Maths

Theoretical and Mathematical Physics

Statistics

Study anywhere. Anytime. Across all devices.

Simplify the given expression. State the excluded values of the variables.
$\frac{16 x^{2} y^{3}}{8 x y}$