# The volume of a rectangular prism is (100x^16y^12z^2). If the length of the prism is 4x^2y^2 and its width is (5x^8y^7z^-2), how do you find the height of the prism y?

Dec 14, 2016

$5 {x}^{6} {y}^{3} {z}^{4}$

#### Explanation:

width*length
$\left(4 {x}^{2} {y}^{2}\right) \left(5 {x}^{8} {y}^{7} {z}^{-} 2\right)$
$= 20 {x}^{10} {y}^{9} {z}^{-} 2$
height=volume÷width multiplied by length
(100x^16y^12z^2)/(20x^10y^9z^-2
$= 5 {x}^{6} {y}^{3} {z}^{4}$=h
check
Volume=width multiplied by length multiplied by height
$\left(5 {x}^{8} {y}^{7} {z}^{-} 2\right) \left(4 {x}^{2} {y}^{2}\right) \left(5 {x}^{6} {y}^{3} {z}^{4}\right)$
$= 100 {x}^{16} {y}^{12} {z}^{2}$