Question

Which expression is equal to (2mn)^4 / (6m^-3n^-2)?

A) 8m^7n^6 / 3
B) 10m^7n^6 / 3
C) 8m^16n^12 / 3
D) m^4n^6 / 3

Answer 1

The expression (2mn)^4 / (6m^-3n^-2) is equal to 96m^7n^6, option A).

Step-by-step explanation:

The expression (2mn)^4 / (6m^-3n^-2) can be simplified as follows:

1. Raising (2mn) to the power of 4, we get (2^4)(m^4)(n^4) = 16m^4n^4.
2. Raising (6m^-3n^-2) to the power of -1, we get (6^-1)(m^-3)(n^-2) = 1/(6m^3n^2).
3. Dividing 16m^4n^4 by 1/(6m^3n^2), we multiply by the reciprocal: 16m^4n^4 * (6m^3n^2/1) = 96m^7n^6.

Therefore, the expression (2mn)^4 / (6m^-3n^-2) is equal to 96m^7n^6, option A).