Question

the vault shown is in the shape of a cube. if each side is 3y^{3} feet, find its volume.
the volume of the vault is
(simplify your answer.)

Explanation:

Step1: Recall the volume formula for a cube

The volume \( V \) of a cube is given by \( V = s^3 \), where \( s \) is the length of a side.

Step2: Substitute the side length into the formula

Here, \( s = 3y^{3} \). So, \( V=(3y^{3})^{3} \).
Using the power - of - a - product rule \((ab)^n=a^{n}b^{n}\), we have \( V = 3^{3}\times(y^{3})^{3}\).

Step3: Simplify the exponents

Since \( 3^{3}=27 \) and using the power - of - a - power rule \((a^{m})^{n}=a^{mn}\), \((y^{3})^{3}=y^{3\times3}=y^{9}\).

Answer:

\(27y^{9}\)