Write an equation describing the relationship of the given variables.
$y$ varies directly as the fourth power of $x$ and when $x=3, y=324$
\(\boxed{y=4x^4}\)
Step 1 :Write an equation describing the relationship of the given variables: $y=kx^4$
Step 2 :Given: when $x=3$, $y=324$
Step 3 :Substitute the given values into the equation: $324=k(3)^4$
Step 4 :Solve for $k$: $k=\frac{324}{3^4}=4.0$
Step 5 :Substitute the value of $k$ back into the equation: $y=4x^4$
Step 6 :\(\boxed{y=4x^4}\)