Answer:
[tex]H = 3x^2y[/tex]
Step-by-step explanation:
Given
[tex]V = 36x&^6y^8[/tex]
[tex]L = 4x^3y^5[/tex]
[tex]W = 3xy^2[/tex]
Required
Find the height of the prism
Volume (V) is calculated as:
[tex]V =LWH[/tex]
Substitute values for V, L and W
[tex]36x^6y^8 =4x^3y^5 * 3xy^2 * H[/tex]
Make H the subject
[tex]H = \frac{36x^6y^8}{4x^3y^5 * 3xy^2}[/tex]
[tex]H = \frac{36x^6y^8}{4*3x^3*x*y^5y^2}[/tex]
[tex]H = \frac{36x^6y^8}{12x^4*y^7}[/tex]
Divide:
[tex]H = 3x^{6-4}y^{8-7}[/tex]
[tex]H = 3x^2y[/tex]
The height of the prism is: [tex]3x^2y[/tex]
