We have two equations:
(√m)⁴ n² = 2304 ----(1)
(√m) n = 12 ----(2)
Let's solve for m and n using these equations.
First, we can simplify equation (1) by expanding (√m)⁴ as m²:
m²n² = 2304
Simplifying further, we get:
mn = ±48 ----(3) (Taking square root on both sides)
Next, we can substitute equation (2) into equation (3) to get:
12√m = ±48
Simplifying further, we get:
√m = ±4
Squaring both sides, we get:
m = 16 or m = 16
So, the value of m is 16.
Now, we can substitute this value of m into equation (2) to get:
√16n = 12
Simplifying further, we get:
4n = 12
Therefore, the value of n is 3.
Hence, the solutions to the given equations are m = 16 and n = 3.