Chapter 7, Problem 19CR

To determine

To complete: given equation.

Answer to Problem 19CR

The complete equation is $x^2{y}^5\cdot x^3{y}^6=x^5{y}^{11}$ .

Explanation of Solution

Given information:

Given equation,

  $x^2{y}^5\cdot x^{}{y}^{}=x^5{y}^{11}$

Calculation:

Let, us consider the missing numbers are $a,b$ .

So, consider the equation,

  $x^2{y}^5\cdot x^a{y}^b=x^5{y}^{11}$

Now, solve the equation as shown,

  $\begin{array}{c}{x}^2{y}^5\cdot x^a{y}^b=x^5{y}^{11}\\ x^{2+a}\cdot y^{5+b}=x^5{y}^{11}\\ 2+a=5\text{or}a=3\\ 5+b=11\text{or}b=6\end{array}$

So, the complete equation is $x^2{y}^5\cdot x^3{y}^6=x^5{y}^{11}$ .