Evaluate the expression when$x= -5, y=3, \text{and} z=2$.

$x^2 y z^2$

When two or more numbers are multiplied together, it gives a number. The numbers that are being multiplied are called the factors. And the result of the multiplication of numbers is called the product of those numbers.

Suppose a, b, and c is three real numbers.

Associative property of Multiplication

Property: $\text{(a} · \text{b)} · \text{c}=\text{a} · ( \text{b} · \text{c} )$

If you are multiplying three real numbers, the product is always the same regardless of their grouping.

Example: $\text{(6} · \text{4)} · \text{3}=\text{6} · ( \text{4} · \text{3} ) = 72$

To evaluate the expression$33xy$, substitute the value of x as – 5 and the value of y as 3 and z as 2 and multiply the numbers as shown below,

localid="1652348647373" $\begin{array}{l}{x}^{2}y{z}^2\\ ={\left(-5\right)}^2·3·2^2\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}Substitute\hspace{0.17em}\hspace{0.17em}}x=-5,y=3\text{\hspace{0.17em}\hspace{0.17em}and\hspace{0.17em}\hspace{0.17em}}z=2\\ =25·3·4\\ =25·(3·4)(\text{Associative\hspace{0.17em}\hspace{0.17em}Property\hspace{0.17em}\hspace{0.17em}of\hspace{0.17em}\hspace{0.17em}Multiplication)}\\ =(25·3)·4(\text{Associative\hspace{0.17em}\hspace{0.17em}Property\hspace{0.17em}\hspace{0.17em}of\hspace{0.17em}\hspace{0.17em}Multiplication)}\\ =75·4=300\end{array}$

Thus, the value of the expression$x^{2}y{z}^2=300$