Solve for the following equation step by step and justify your steps when using an exponential property. (7^x) ^4=7^2-7^3/7^3x

The equation is (7^x) ^4 = (7^2 * 7^3) / 7^3x

(7^x) ^4 is equal to 7^ (4x)

7^2 * 7^3 is equal to 7^ (2+3) which gives 7^5

therefore;

7^5/7^3x is equal to 7^ (5-3x)

Hence we get;

7^ (4x) = 7^ (5-3x)

thus; 4x = 5-3x

7x = 5 (solving for x)

Therefore; x = 5/7