Answer:
The volume of the cube is [tex]\mathit{\frac{27}{z^3x^{9}}}[/tex] cu in.
Step-by-step explanation:
The Volume of a Cube
Let's have a cube of side length a. The volume of the cube is:
[tex]V=a^3[/tex]
The cube of the image has a side length of
[tex]\displaystyle a=\frac{3x^{-3}}{z}\ inches[/tex]
Simplifying the expression of the base by converting the negative exponent in the numerator to the denominator:
[tex]\displaystyle a=\frac{3}{zx^{3}}\ inches[/tex]
Now find the volume:
[tex]\displaystyle V=\left(\frac{3}{zx^{3}}\ inches\right)^3[/tex]
Applying the exponents:
[tex]\displaystyle V=\frac{3^3}{z^3x^{9}}\ inches^3[/tex]
[tex]\displaystyle V=\frac{27}{z^3x^{9}}\ inches^3[/tex]
The volume of the cube is [tex]\mathbf{\frac{27}{z^3x^{9}}}[/tex] cu in.
