How do you simplify ${\left( { - 2{y^3}z} \right)^3}$?

Hint: To simplify this question , we need to solve it step by step . starting from the parentheses with exponent over it , this means that the number $ - 2{y^3}z$ the number which can be expressed as is having a cube over it also . We should first write the cube of 2 also ‘ z ’ in its cube form and then the cube of ${y^3}$ which will be the cube of the cube . Then simplify it to get the desired answer .

Complete step-by-step answer:
The number with whole exponent as cube can be expressed as the number with exponent by writing their respective cube that is for any number also for the number having exponent on exponent will be solved as follows =${\left( {{p^n}} \right)^n} = {p^{n \times n}}$, p is number base and n is the exponent which is multiplied to the exponent over it .
 So , calculating the cube of the respective numbers
 \[
= {( - 2{y^3}z)^3} \\
   = {( - 2)^3} = - 8 \\
   = {({y^3})^3} = {y^{3 \times 3}} = {y^9} \\
   = {(z)^3} = {z^3} \;
 \]
And then combining all the respective cubed terms to make our question solved = $ - 8{y^9}{z^3}$.
This is also the simplified solution to the question .
Therefore , the reduced form is $ - 8{y^9}{z^3}$. It is already in its simplest form .
So, the correct answer is “ $ - 8{y^9}{z^3}$”.

Note: You should always remember that the square of -1 or any negative number will become positive .
But the cube of the negative number will always remain negative .
Greatest common factor itself describes the number which has a common factor , there is only one common factor that means the number is already simplified .