# How do you write the equation if F varies inversely as the cube root of S and S = 64 when F = 4?

Jun 15, 2015

$F = \frac{16}{{S}^{\frac{1}{3}}}$

#### Explanation:

We just write the equation with constant of proportion $k$

$F = \frac{k}{{S}^{\frac{1}{3}}}$

And evaluate it in $F = 4$ and $S = 64 = {2}^{6}$, and solve the equation for k.

$4 = \frac{k}{{2}^{\frac{6}{3}}} \implies k = 16$