Product of exponents in chain of equations

Using sequential substitution: $4 = 3^a$ $5 = 4^b = (3^a)^b = 3^{ab}$ $6 = 5^c = (3^{ab})^c = 3^{abc}$ $7 = 6^d = 3^{abcd}$ $8 = 7^e = 3^{abcde}$ $9 = 8^f = 3^{abcdef}$

Since $9 = 3^2$, we have: $3^{abcdef} = 3^2 \implies abcdef = 2$