Answer:
[tex]\displaystyle L=4x^{4}y^{8}z^{12}[/tex]
Step-by-step explanation:
The Volume of Rectangular Prism
Given a rectangular prism of width W, height H, and length L, its volume is calculated as follows:
V = WHL
We are given the volume of a rectangular prism:
[tex]V=72x^8y^{14}z^{22}[/tex]
It's also known the width is:
[tex]W=6x^3y[/tex]
And height
[tex]H=3xy^5z^{10}[/tex]
Substituting in the formula, we solve for L:
[tex]72x^8y^{14}z^{22}=(6x^3y)*(3xy^5z^{10})L[/tex]
[tex]\displaystyle L=\frac{72x^8y^{14}z^{22}}{(6x^3y)*(3xy^5z^{10})}[/tex]
Operating the denominator
[tex]\displaystyle L=\frac{78x^8y^{14}z^{22}}{18x^4y^6z^{10}}[/tex]
Dividing:
[tex]\displaystyle L=4x^{8-4}y^{14-6}z^{22-10}[/tex]
Simplifying:
[tex]\boxed{\displaystyle L=4x^{4}y^{8}z^{12}}[/tex]
