Why isn't it B cubed?

Algebra Level 4

$\dfrac{1}{a^4}+\dfrac{1}{b^4}+\dfrac{1}{c^4}=1$

Given the above equation for positive numbers $a,b,c$ .

Find the minimum value of

$\dfrac{a^4b^4+a^4c^4+b^4c^4}{a^3b^2c^3}$

If the minimum value of the above is $x$ , input your answer as $\lfloor 100x \rfloor$ .

This is part of the set Trevor's Ten

Details and Assumptions