Chapter 5.4, Problem 3MCQ

To determine

To Evaluate: The simplified form of the expression $\frac{3a^4{b}^{3}c}{6a^2{b}^5{c}^3}$ where $a\ne 0,b\ne 0,c\ne 0$ .

Answer to Problem 3MCQ

The value of the expression $\frac{3a^4{b}^{3}c}{6a^2{b}^5{c}^3}$ is $\frac{a^2}{2b^2{c}^2}$.

Explanation of Solution

Given information:

The expression is $\frac{3a^4{b}^{3}c}{6a^2{b}^5{c}^3}$ .

Formula used:

For any real value $x$ and integer $a$ , $b$ , if $x\ne 0$ the quotient of power property states as $\frac{x^b}{x^a}=x^{b-a}$

For any real value $x$ and integer $a$ , the negative exponent of $x$ that is $x^{-a}$ rewrite as $\frac{1}{x^a}$ .

Calculation:

Consider the expression is $\frac{3a^4{b}^{3}c}{6a^2{b}^5{c}^3}$ .

Recall that for any real value $x$ and integer $a$ , $b$ , if $x\ne 0$ the quotient of power property states as $\frac{x^b}{x^a}=x^{b-a}$

Apply it,

  $\begin{array}{c}\frac{3a^4{b}^{3}c}{6a^2{b}^5{c}^3}=\frac{3}{6}{a}^{4-2}{b}^{3-5}{c}^{1-3}\\ =\frac{1}{2}{a}^2{b}^{-2}{c}^{-2}\end{array}$

Again recall that for any real value $x$ and integer $a$ , $b$ , if $x\ne 0$ the quotient of power property states as $\frac{x^b}{x^a}=x^{b-a}$

Use it,

  $\frac{1}{2}{a}^2{b}^{-2}{c}^{-2}=\frac{a^2}{2b^2{c}^2}$

Thus, the value of the expression $\frac{3a^4{b}^{3}c}{6a^2{b}^5{c}^3}$ is $\frac{a^2}{2b^2{c}^2}$ .