Simplify 3 (2m^3n^-2) ^4

(48 m^12) / n^8

Step-by-step explanation:

Simplify the following:

3 ((2 m^3) / (n^2)) ^4

Multiply each exponent in (2 m^3) / (n^2) by 4:

3*2^4 m^ (4*3) n^ (-2*4)

4 (-2) = - 8:

3*2^4 m^ (4*3) n^ (-8)

4*3 = 12:

(3*2^4 m^12) / (n^8)

2^4 = (2^2) ^2:

(3 (2^2) ^2 m^12) / (n^8)

2^2 = 4:

(3*4^2 m^12) / (n^8)

4^2 = 16:

(3*16 m^12) / (n^8)

3*16 = 48:

Answer: (48 m^12) / n^8