Solve for $x$ : \[ x=10^{7 \log _{10} 6-\log _{10} 3} \] \[ x= \] Note: Your answer must be exact and in simplest form.

Step 1 ：Given the equation \(x=10^{7 \log _{10} 6-\log _{10} 3}\)

Step 2 ：We can simplify the equation using the properties of logarithms

Step 3 ：Using the property \(a^{log_a b} = b\), we can rewrite the equation as \(x = 10^{7 \log _{10} 6} / 10^{\log _{10} 3}\)

Step 4 ：Further simplifying, we get \(x = (10^{\log _{10} 6})^7 / 3\)

Step 5 ：Finally, we get \(x = 6^7 / 3\)

Step 6 ：So, the solution to the equation is \(x=\boxed{\frac{6^7}{3}}\)