Chapter 4.3, Problem 16WE

To determine

To Simplify: The expression $\left(3y^{3}z\right)\left(4y^4{z}^2\right)$

Answer to Problem 16WE

The required answer is $12y^7{z}^3$ .

Explanation of Solution

Given information:

The expression $\left(3y^{3}z\right)\left(4y^4{z}^2\right)$

Concept Used:

Rule of exponents for product of powers states that to multiply two powers with same base, the exponents are added.

For example $a^m\cdot a^n=a^{m+n}$

Commutative property of multiplication states that the product of any numbers remains the same irrespective of the order in which we multiply.

For example:

  $2\cdot 5=5\cdot 2=10$

Associative property of multiplication states that the product of the any numbers remains the same regardless of the grouping of factors.

For example:

  $2\left(5\cdot 3\right)=\left(2\cdot 5\right)\cdot 3=30$

Calculation:

  $\left(3y^{3}z\right)\left(4y^4{z}^2\right)$

Commutative and Associative property of multiplication.

  $=\left(3\cdot 4\right)\left(y^3\cdot y^4\right)\left(z\cdot z^2\right)$

Using rule of exponents for product of powers

  $\begin{array}{l}=12y^{3+4}{z}^{1+2}\\ =12y^7{z}^3\end{array}$