Question

the vault shown is in the shape of a cube. if each side is 4y² 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 with side length \( s \) is given by the formula \( V = s^3 \).

Step2: Substitute the given side length into the formula

Here, the side length \( s = 4y^2 \) feet. So we need to calculate \( (4y^2)^3 \).
Using the power of a product rule \((ab)^n=a^n b^n\) and the power of a power rule \((a^m)^n=a^{mn}\), we have:
\((4y^2)^3 = 4^3\times(y^2)^3\)
\(4^3 = 64\) and \((y^2)^3 = y^{2\times3}=y^6\)
So, \((4y^2)^3 = 64y^6\)

Answer:

The volume of the vault is \( 64y^6 \) cubic feet.