Question

the volume of a rectangular prism is (100x¹⁸y¹²z²). if the length of the prism is (4x²y²) and the width is (5x⁸y⁷z-²), find the height of the prism.

Answer 1

We have the following rectangular prism,:

Given that we know the value of the volume, we can find the height using the following formula:

$\begin{gathered} V=a\cdot b\cdot h \\ V=100x^8y^{12}z^2 \\ a=4x^2y^2 \\ b=5x^8y^7z^{-2} \\ \Rightarrow100x^{8^{}}y^{12}z^2=(4x^2y^2)(5x^8y^7z^{-2})\cdot h \end{gathered}$

Now we multiply both factors using the rules of exponents to get the following:

$\begin{gathered} 100x^8y^{12}z^2=(4x^2y^2)(5x^8y^7z^{-2})\cdot h=(20x^{8+2}y^{2+7}z^{-2})\cdot h \\ \Rightarrow100x^{8^{}}y^{12}z^2=(20x^{10}y^9z^{-2})\cdot h \end{gathered}$

finally, we solve for h and again we use the rules of exponents on the resulting division:

$\begin{gathered} h=\frac{100x^8y^{12}z^2}{20x^{10}y^9z^{-2}}=5x^{8-10}y^{12-9}z^{2-(-2)} \\ h=5x^{-2}y^3z^4 \end{gathered}$

therefore, the height of the prism is h=5x^(-2)y^3z^4