Chapter 5.4, Problem 1MCQ

To determine

To Evaluate: The simplified form of the expression $\left(3x^2{y}^{-3}\right)\left(-2x^3{y}^5\right)$ where $x\ne 0,y\ne 0$ .

Answer to Problem 1MCQ

The value of the expression $\left(3x^2{y}^{-3}\right)\left(-2x^3{y}^5\right)$ is $-6x^5{y}^2$ .

Explanation of Solution

Given information:

The expression is $\left(3x^2{y}^{-3}\right)\left(-2x^3{y}^5\right)$ .

Formula used:

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

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

Calculation:

Consider the expression is $\left(3x^2{y}^{-3}\right)\left(-2x^3{y}^5\right)$ .

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

Apply it,

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

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

Again use it,

  $\begin{array}{c}\left(3x^2\frac{1}{y^3}\right)\left(-2x^3{y}^5\right)=3\times \left(-2\right)x^{2+3}y\\ =-6x^5{y}^2\end{array}$

Thus, the value of the expression $\left(3x^2{y}^{-3}\right)\left(-2x^3{y}^5\right)$ is $-6x^5{y}^2$ .