The explicit ABC conjecture with exponent $7/4$

Let $A$, $B$, and $C$ be positive integers such that $A+B=C$ and $(A,B)=1$. Define $\operatorname{rad}(ABC)$ to be the product of the distinct prime divisors of $ABC$. Explicit ABC conjecture. Then

$$\max(A,B,C)<\operatorname{rad}(ABC)^{7/4}.$$

This is a specific, stronger-than-standard explicit form of the ABC conjecture invoked to constrain even perfect numbers that are sums of two high-degree powers. Its truth is not established, so the resulting conditional consequences for perfect numbers do not settle the unconditional problem.