Chapter 7.1, Problem 71PFA

To determine

To find: The expression simplifies to the monomial $12h^6{j}^8$

  $\begin{array}{l}\left(A\right)\left(4h^2{j}^4\right)\left(3h^3{j}^2\right)\\ \left(B\right)\left(2h^3{j}^2\right)\left(6h^3{j}^4\right)\\ \left(C\right)\left(3h^3{j}^6\right)\left(4h^3{j}^2\right)\\ \left(D\right)\frac{\left(8h^2{j}^4\right)\left(3h^3{j}^2\right)}{2}\end{array}$

Answer to Problem 71PFA

The required expression that simplifies to the monomial $12h^6{j}^8$ is option $\left(C\right)\left(3h^3{j}^6\right)\left(4h^3{j}^2\right)$ .

Explanation of Solution

Given information:

The given expression $12h^6{j}^8$

Calculation:

Let us take the option $\left(C\right)\left(3h^3{j}^6\right)\left(4h^3{j}^2\right)$

Therefore, $\left(3h^3{j}^6\right)\left(4h^3{j}^2\right)$

  $=\left(3\cdot 4\right)\left(h^3\cdot h^3\right)\left(j^6\cdot j^2\right)$

(Group the coefficient and variables)

  $=\left(3\cdot 4\right)\left(h^{3+3}\right)\left(j^{6+2}\right)$

(Product of the powers)

  $=12h^6{j}^8$

(Simplify)

So, the required expression is $\left(3h^3{j}^6\right)\left(4h^3{j}^2\right)$