## Algebra: A Combined Approach (4th Edition)

$27y^{12}$
We are given that the vault has a length, width, and height of $3y^{4}$ feet. We know that the volume of a cube is calculated as $v=l\times w\times h$. Based on the product rule for exponents, we know that $a^{m}\times a^{n}=a^{m+n}$ (where $m$ and $n$ are positive integers and $a$ is a real number). Therefore, $volume=3y^{4}\times3y^{4}\times3y^{4}=3^{1+1+1}\times y^{4+4+4}=3^{3}y^{12}=27y^{12}$.