So the question asks:

(a) Draw the Feynman diagrams showing the dominant leptonic decay mode of the $\mu^-$ and the $\tau^-$.

(b) Assuming $m_\tau \gg m_\mu \gg m_e$, estimate the ratio of the rate of the two decay modes.

Part (a) is simple.

Part (b), I'm not sure what I am meant to do. I know the decay widths for the decay modes are $$ \Gamma(\mu^- \to e^-+\bar{\nu}_e+\nu_\mu) = \frac{G_F^eG_F^\mu m_\mu^5}{192 \pi^3}, $$ $$ \Gamma(\tau^- \to e^-+\bar{\nu}_e+\nu_\tau) = \frac{G_F^eG_F^\tau m_\tau^5}{192 \pi^3}, $$ $$ \Gamma(\tau^- \to \mu^-+\bar{\nu}_\mu+\nu_\tau) = \frac{G_F^\mu G_F^\tau m_\tau^5}{192 \pi^3} $$

and by lepton universality, $$ G_F^e=G_F^\mu = G_F^\tau. $$

I'm not sure how to proceed from here. Is it simply finding the branching ratios and dividing one by the other?