For a base B and natural number q, we interpret B^(1/q) as the qth root of B. That makes sense because [B^(1/q)]^q should just be B^1 = B, following the power rule. For any fraction p/q, we then interpret B^(p/q) as [B^(1/q)]^p, the pth power of B^(1/q), again inspired by the power rule.