If $7^{4x}=343$, what is the value of $7^{4x-3}$?
I notice that $343=7^3$, so I can rewrite the equation as $7^{4x}=7^3$. This means that the exponents must be equal, so $4x=3$. Solving for x, I get $x=\frac{3}{4}$. Now I can plug this into the expression $7^{4x-3}$. I get $7^{4(\frac{3}{4})-3}=7^{3-3}=7^0$. I know that any nonzero number raised to the zero power is 1, so $7^0=1$. 