Determine the simplified form of the equation: $7 \sqrt{144 x^{3}}$

Step 1 ：The given equation is $7 \sqrt{144 x^{3}}$

Step 2 ：Take the square root of 144 and $x^{3}$

Step 3 ：The square root of 144 is 12 and the square root of $x^{3}$ is $x^{1.5}$

Step 4 ：Multiply these results by 7

Step 5 ：The simplified form of the equation is $\boxed{84x^{1.5}}$