Which equation is equivalent to f(x)=16x^4-81=0

I'm pretty sure you are looking for factored forms as an equivalent equation, so here is how you do it. 
This equation would be solved by difference of squares. 16, x^4, and 81 are all perfect squares ( which means that it is a number multiplied by itself, 16 is 4 x4 for example). So the first thing you want to do is recall the formula which is
(a^2 - b^2) = (a - b)*(a + b) 
(16x^4 - 81)= 0
Find the sq. root of 16 which is 4, and of x^4 which is x^2, and 81 which is 9. Now re write it in the (a - b)*(a + b) format. > (4x^2 - 9)*(4x^2 + 9) = 0